Exhibit 99.1

For Immediate Release

May 2, 2013

Approach Resources Inc.

Reports First Quarter 2013 Results

Fort Worth, Texas, May 2, 2013 – Approach Resources Inc. (NASDAQ: AREX) today reported results for first quarter 2013. Highlights for first quarter 2013, compared to first quarter 2012, include:

| • |  | Production up 15% to 8.4 MBoe/d, and oil production up 63% to 310 MBbls

| • |  | Revenues increased 19% to $36.3 million

| • |  | Net loss of $347,000, or $0.01 per diluted share

| • |  | Adjusted net income (non-GAAP) of $2.4 million, or $0.06 per diluted share

| • |  | EBITDAX (non-GAAP) increased 17% to $24.4 million, or $0.63 per diluted share

| • |  | Borrowing base increased to $315 million on May 1 st

Production for first quarter 2013 totaled 754 MBoe (8.4 MBoe/d), compared to production of 654 MBoe (7.2 MBoe/d) in first quarter 2012, a 15% increase. Oil production for first quarter 2013 increased 63% to 310 MBbls, compared to 191 MBbls produced in first quarter 2012. Production for first quarter 2013 was 41% oil, 28% NGLs and 31% natural gas, compared to 29% oil, 33% NGLs and 38% natural gas in first quarter 2012. As previously reported, estimated production for first quarter 2013 was impacted by a third-party NGL fractionation facility’s repair and maintenance.

Management Comment

J. Ross Craft, the Company’s President and CEO, commented, “We are encouraged by the improvement in our per-unit costs this quarter compared to fourth quarter 2012. In addition, we continue to see our horizontal well costs trend lower. Horizontal drilling and completion costs for first quarter 2013 averaged approximately $6.1 million per well, down from $6.4 million for the second half of 2012. We’re also encouraged by the initial results from our stacked wellbore pilot program and from our ongoing development in the horizontal Wolfcamp shale play. We plan to continue testing multi-bench development in Project Pangea, including testing optimal well spacing and drilling pattern, to maximize recoveries, efficiencies and savings.”

First Quarter 2013 Financial Results

Net loss for first quarter 2013 was $347,000, or $0.01 per diluted share, on revenues of $36.3 million. This compares to net income for first quarter 2012 of $1.7 million, or $0.05 per diluted share, on revenues of $30.6 million. First quarter 2013 revenues increased $5.7 million due to an increase in production volumes and gas price realizations ($10.9 million), partially offset by a decrease in oil and NGL price realizations ($5.2 million). Net loss for first quarter 2013 included an unrealized loss on commodity derivatives of $4.1 million and a realized gain on commodity derivatives of $307,000.

Excluding the unrealized loss on commodity derivatives and related income tax effect, adjusted net income (non-GAAP) for first quarter 2013 was $2.4 million, or $0.06 per diluted share, compared to $3.5 million, or $0.10 per diluted share, for first quarter 2012. See “Supplemental Non-GAAP Financial and Other Measures” below for our reconciliation of adjusted net income to net (loss) income.

EBITDAX (non-GAAP) for first quarter 2013 was $24.4 million, or $0.63 per diluted share, compared to $20.8 million, or $0.62 per diluted share, for first quarter 2012. See “Supplemental Non-GAAP Financial and Other Measures” below for our reconciliation of EBITDAX to net (loss) income.

Average realized commodity prices for first quarter 2013, before the effect of commodity derivatives, were $82.01/Bbl of oil, $29.17/Bbl of NGLs and $3.32/Mcf of natural gas, compared to $94.39/Bbl of oil, $42.50/Bbl of NGLs and $2.35/Mcf of natural gas for first quarter 2012. Our average realized price, including the effect of commodity derivatives, was $48.51/Boe for first quarter 2013, up 5% compared to $46.10/Boe for first quarter 2012.

Our average realized oil price was impacted by the regional Midland/Cushing differential during first quarter 2013. For first quarter 2013, our average realized oil price, excluding oil derivatives, of $82.01/Bbl reflected a regional and transportation differential of approximately $12.37/Bbl below NYMEX WTI. On April 3, 2013, we began flowing oil down our joint venture pipeline. As a result of our current outlook for the Midland/Cushing differential, our differential derivative position and transporting our oil production by pipeline, we expect our oil differential will decrease for the remainder of 2013.

Lease operating expenses (“LOE”) increased in first quarter 2013 compared to first quarter 2012 primarily due to higher well repair, maintenance and water hauling expenses. Production and ad valorem taxes increased from the prior year quarter due to our increase in oil, NGL and gas sales. General and administrative expenses (“G&A”) increased from the prior year quarter primarily due to higher salaries and benefits, a result of increased staffing. Depletion, depreciation and amortization expense (“DD&A”) increased from the prior year quarter primarily due to higher production and oil and gas property carrying costs, relative to estimated proved developed reserves. Higher oil and gas property carrying costs primarily reflect our development of our oil-focused Wolfcamp shale play.

LOE, G&A and DD&A per Boe decreased in first quarter 2013, compared to fourth quarter 2012. In addition, LOE per Boe decreased for the second quarter in a row. Overall, costs decreased 10.5% sequentially. The following table is a summary of first quarter 2013 expenses per Boe, compared to fourth quarter 2012.

Costs and expenses (per Boe): |  | 1Q13 |  |  | 4Q12 |  |  | Percent Change |
LOE |  | $ | 7.14 |  |  | $ | 7.29 |  |  |  | (2.1 | )%
Production and ad valorem taxes |  |  | 3.39 |  |  |  | 3.12 |  |  |  | 8.7 | %
Exploration |  |  | 0.34 |  |  |  | 2.72 |  |  |  | (87.5 | )%
G&A |  |  | 8.50 |  |  |  | 10.79 |  |  |  | (21.2 | )%
DD&A |  |  | 22.62 |  |  |  | 22.99 |  |  |  | (1.6 | )%
Total |  | $ | 41.99 |  |  | $ | 46.91 |  |  |  | (10.5 | )%

Operations Update

During first quarter 2013, we drilled 10 wells and completed five wells, including three wells that were waiting on completion at December 31, 2012. At March 31, 2013, 12 wells were in progress or waiting on completion, of which five wells were completed and turned to sales shortly after March 31, 2013. We expect second quarter production to range from 9.3 MBoe/d to 9.6 MBoe/d.

We currently have three horizontal rigs drilling in Project Pangea, and our program for testing multi-bench development is underway. During first quarter 2013, we targeted the Wolfcamp A and B

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benches with two stacked wellbores in Pangea West. These two wells were drilled from a single pad, completed with 26 stages and flowed at an initial production rate ranging from 705 Boe/d to 843 Boe/d, with an average oil cut of 94%. These are our best wells drilled and completed in Pangea West to date based on initial performance.

Also, in north Project Pangea, we targeted the Wolfcamp A and B benches with four stacked wellbores. These four wells were drilled in a chevron pattern, completed with 26 to 27 stages and flowed at an initial production rate ranging from 366 Boe/d to 701 Boe/d, with an average oil cut of 84%.

2013 Capital Expenditures

Costs incurred during first quarter 2013 totaled $69.5 million, consisting of $61.8 million for drilling and completion activities, $6.7 million for pipeline, infrastructure projects and other equipment and $1 million for acreage acquisitions and extensions and 3-D seismic data acquisition. Approximately $60.6 million of the $61.8 million for drilling and completion activities includes capital for drilling nine horizontal wells and completing 10 horizontal wells. Also, in first quarter 2013, we made a capital contribution to our pipeline joint venture of $6.3 million for oil pipeline and facilities construction.

Liquidity and Commodity Derivatives Update

At March 31, 2013, we had a $300 million revolving credit agreement with a $280 million borrowing base and $152.3 million outstanding. At March 31, 2013, our liquidity and long-term debt-to-capital ratio were $128 million and 19.3%, respectively. See “Supplemental Non-GAAP Financial and Other Measures” below for our calculation of “liquidity” and “long-term debt-to-capital ratio.”

The lenders under our revolving credit agreement completed their semi-annual borrowing base redetermination, resulting in an increase to the borrowing base to $315 million from $280 million. In addition, the total facility amount increased to $500 million from $300 million and the term was extended to July 31, 2016, from July 31, 2014. Pro forma for the borrowing base increase, our liquidity was $163 million at March 31, 2013.

We enter into commodity derivatives positions to manage our exposure to commodity price fluctuations. Please refer to the “Unaudited Commodity Derivatives Information” table below for a detailed summary of the Company’s current derivatives positions.

First Quarter 2013 Conference Call

Approach will host a conference call on Friday, May 3, 2013, at 10:00 a.m. Central Time (11:00 a.m. Eastern Time) to discuss first quarter 2013 financial and operating results. To participate in the conference call, domestic participants should dial (866) 783-2138 and international participants should dial (857) 350-1597 approximately 15 minutes before the scheduled conference time. To access the simultaneous webcast of the conference call, please visit the Calendar of Events page under the Investor Relations section of the Company’s website, www.approachresources.com, 15 minutes before the scheduled conference time to register for the webcast and install any necessary software. The webcast will be archived for replay on the Company’s website until August 1, 2013.

In addition, the Company will host a telephone replay of the call, which will be available for one week. U.S. callers may access the telephone replay by dialing (888) 286-8010 and international callers may dial (617) 801-6888. The passcode is 12626307.

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Approach Resources Inc. is an independent oil and gas company with core operations, production and reserves located in the Permian Basin in West Texas. The Company targets multiple oil and liquids-rich formations in the Permian Basin, where the Company operates approximately 148,000 net acres. For more information about the Company, please visit www.approachresources.com. Please note that the Company routinely posts important information about the Company under the Investor Relations section of its website.

Forward-Looking and Cautionary Statements

This press release contains forward-looking statements within the meaning of Section 27A of the Securities Act of 1933 and Section 21E of the Securities Exchange Act of 1934. All statements, other than statements of historical facts, included in this press release that address activities, events or developments that the Company expects, believes or anticipates will or may occur in the future are forward-looking statements. Without limiting the generality of the foregoing, forward-looking statements contained in this press release specifically include anticipated financial and operational results of the Company, including production guidance. These statements are based on certain assumptions made by the Company based on management’s experience, perception of historical trends and technical analyses, current conditions, anticipated future developments and other factors believed to be appropriate and reasonable by management. When used in this press release, the words “will,” “potential,” “believe,” “estimate,” “intend,” “expect,” “may,” “should,” “anticipate,” “could,” “plan,” “predict,” “project,” “profile,” “model” or their negatives, other similar expressions or the statements that include those words, are intended to identify forward-looking statements, although not all forward-looking statements contain such identifying words. Such statements are subject to a number of assumptions, risks and uncertainties, many of which are beyond the control of the Company, which may cause actual results to differ materially from those implied or expressed by the forward-looking statements. Further information on such assumptions, risks and uncertainties is available in the Company’s Securities and Exchange Commission (“SEC”) filings. The Company’s SEC filings are available on the Company’s website at www.approachresources.com. Any forward-looking statement speaks only as of the date on which such statement is made and the Company undertakes no obligation to correct or update any forward-looking statement, whether as a result of new information, future events or otherwise, except as required by applicable law.

For a glossary of oil and gas terms and abbreviations used in this release, please see our Annual Report on Form 10-K filed with the SEC on February 28, 2013.

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UNAUDITED RESULTS OF OPERATIONS

|  | Three Months Ended March 31, |
|  | 2013 |  |  | 2012 |
Revenues (in thousands): |  |  |  |  |  |  |  |
Oil |  | $ | 25,462 |  |  | $ | 18,006 |
NGLs |  |  | 6,237 |  |  |  | 9,107 |
Gas |  |  | 4,570 |  |  |  | 3,505 |
Total oil, NGL and gas sales |  |  | 36,269 |  |  |  | 30,618 |
Realized gain (loss) on commodity derivatives |  |  | 307 |  |  |  | (484 | )
Total oil, NGL and gas sales including derivative impact |  | $ | 36,576 |  |  | $ | 30,134 |
Production: |  |  |  |  |  |  |  |
Oil (MBbls) |  |  | 310 |  |  |  | 191 |
NGLs (MBbls) |  |  | 214 |  |  |  | 214 |
Gas (MMcf) |  |  | 1,378 |  |  |  | 1,492 |
Total (MBoe) |  |  | 754 |  |  |  | 654 |
Total (MBoe/d) |  |  | 8.4 |  |  |  | 7.2 |
Average prices: |  |  |  |  |  |  |  |
Oil (per Bbl) |  | $ | 82.01 |  |  | $ | 94.39 |
NGLs (per Bbl) |  |  | 29.17 |  |  |  | 42.50 |
Gas (per Mcf) |  |  | 3.32 |  |  |  | 2.35 |
Total (per Boe) |  |  | 48.10 |  |  |  | 46.84 |
Realized gain (loss) on commodity derivatives (per Boe) |  |  | 0.41 |  |  |  | (0.74 | )
Total including derivative impact (per Boe) |  | $ | 48.51 |  |  | $ | 46.10 |
Costs and expenses (per Boe): |  |  |  |  |  |  |  |
Lease operating |  | $ | 7.14 |  |  | $ | 5.48 |
Production and ad valorem |  |  | 3.39 |  |  |  | 3.39 |
Exploration |  |  | 0.34 |  |  |  | 1.97 |
General and administrative |  |  | 8.50 |  |  |  | 8.82 |
Depletion, depreciation and amortization |  |  | 22.62 |  |  |  | 16.87 |

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APPROACH RESOURCES INC. AND SUBSIDIARIES

UNAUDITED CONSOLIDATED STATEMENTS OF OPERATIONS

(In thousands, except shares and per-share amounts)

|  | Three Months Ended March 31, |
|  | 2013 |  |  | 2012 |
REVENUES: |  |  |  |  |  |  |  |
Oil, NGL and gas sales |  | $ | 36,269 |  |  | $ | 30,618 |
EXPENSES: |  |  |  |  |  |  |  |
Lease operating |  |  | 5,383 |  |  |  | 3,580 |
Production and ad valorem taxes |  |  | 2,556 |  |  |  | 2,218 |
Exploration |  |  | 260 |  |  |  | 1,287 |
General and administrative |  |  | 6,410 |  |  |  | 5,764 |
Depletion, depreciation and amortization |  |  | 17,056 |  |  |  | 11,030 |
Total expenses |  |  | 31,665 |  |  |  | 23,879 |
OPERATING INCOME |  |  | 4,604 |  |  |  | 6,739 |
OTHER: |  |  |  |  |  |  |  |
Interest expense, net |  |  | (1,229 | ) |  |  | (887 | )
Equity in losses of investee |  |  | (116 | ) |  |  | — |
Realized gain (loss) on commodity derivatives |  |  | 307 |  |  |  | (484 | )
Unrealized loss on commodity derivatives |  |  | (4,100 | ) |  |  | (2,672 | )
(LOSS) INCOME BEFORE INCOME TAX (BENEFIT) PROVISION |  |  | (534 | ) |  |  | 2,696 |
INCOME TAX (BENEFIT) PROVISION |  |  | (187 | ) |  |  | 982 |
NET (LOSS) INCOME |  | $ | (347 | ) |  | $ | 1,714 |
(LOSS) EARNINGS PER SHARE: |  |  |  |  |  |  |  |
Basic |  | $ | (0.01 | ) |  | $ | 0.05 |
Diluted |  | $ | (0.01 | ) |  | $ | 0.05 |
WEIGHTED AVERAGE SHARES OUTSTANDING: |  |  |  |  |  |  |  |
Basic |  |  | 38,924,163 |  |  |  | 33,249,769 |
Diluted |  |  | 38,924,163 |  |  |  | 33,437,682 |

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UNAUDITED SELECTED FINANCIAL DATA

Unaudited Consolidated Balance Sheet Data |  | March 31, |  |  | December 31, |
(in thousands) |  | 2013 |  |  | 2012 |
Cash and cash equivalents |  | $ | 594 |  |  | $ | 767 |
Other current assets |  |  | 12,018 |  |  |  | 14,889 |
Property and equipment, net, successful efforts method |  |  | 881,008 |  |  |  | 828,467 |
Equity method investment |  |  | 16,056 |  |  |  | 9,892 |
Other assets |  |  | 1,406 |  |  |  | 1,724 |
Total assets |  | $ | 911,082 |  |  | $ | 855,739 |
Current liabilities |  | $ | 66,289 |  |  | $ | 60,247 |
Long-term debt |  |  | 152,250 |  |  |  | 106,000 |
Other long-term liabilities |  |  | 57,332 |  |  |  | 56,024 |
Stockholders’ equity |  |  | 635,211 |  |  |  | 633,468 |
Total liabilities and stockholders’ equity |  | $ | 911,082 |  |  | $ | 855,739 |

Unaudited Consolidated Cash Flow Data |  | Three Months Ended March 31, |
(in thousands) |  | 2013 |  |  | 2012 |
Net cash provided (used) by: |  |  |  |  |  |  |  |
Operating activities |  | $ | 29,638 |  |  | $ | 35,491 |
Investing activities |  | $ | (75,986 | ) |  | $ | (77,665 | )
Financing activities |  | $ | 46,175 |  |  | $ | 42,348 |

UNAUDITED COMMODITY DERIVATIVES INFORMATION

Commodity and Period |  | Contract Type |  | Volume Transacted |  |  | Contract Price
Crude Oil |  |  |  |  |  |  |  |
2013 |  | Collar |  |  | 650 Bbls/d |  |  | $90.00/Bbl – $105.80/Bbl
2013 |  | Collar |  |  | 450 Bbls/d |  |  | $90.00/Bbl – $101.45/Bbl
2013 (1) |  | Collar |  |  | 1,200 Bbls/d |  |  | $90.35/Bbl – $100.35/Bbl
2014 |  | Collar |  |  | 550 Bbls/d |  |  | $90.00/Bbl – $105.50/Bbl
Crude Oil Basis Differential (Midland/Cushing) |  |  |
2013 (2) |  | Swap |  |  | 2,300 Bbls/d |  |  | $1.10/Bbl
Natural Gas |  |  |  |  |  |  |  |
2013 |  | Swap |  |  | 200,000 MMBtu/month |  |  | $3.54/MMBtu
2013 |  | Swap |  |  | 190,000 MMBtu/month |  |  | $3.80/MMBtu
2013 (3) |  | Collar |  |  | 100,000 MMBtu/month |  |  | $4.00/MMBtu – $4.36/MMBtu
2014 |  | Swap |  |  | 360,000 MMBtu/month |  |  | $4.18/MMBtu

(1) | February 2013 – December 2013

(2) | March 2013 – December 2013

(3) | May 2013 – December 2013

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Supplemental Non-GAAP Financial and Other Measures

This release contains certain financial measures that are non-GAAP measures. We have provided reconciliations below of the non-GAAP financial measures to the most directly comparable GAAP financial measures and on the Non-GAAP Financial Information page in the Investor Relations section of our website at www.approachresources.com.

Adjusted Net Income

This release contains the non-GAAP financial measures adjusted net income and adjusted net income per diluted share, which excludes an unrealized loss on commodity derivatives and the related income tax effect. The amounts included in the calculation of adjusted net income and adjusted net income per diluted share below were computed in accordance with GAAP. We believe adjusted net income and adjusted net income per diluted share are useful to investors because they provide readers with a more meaningful measure of our profitability before recording certain items whose timing or amount cannot be reasonably determined. However, these measures are provided in addition to, and not as an alternative for, and should be read in conjunction with, the information contained in our financial statements prepared in accordance with GAAP (including the notes), included in our SEC filings and posted on our website.

The table below provides a reconciliation of adjusted net income to net (loss) income for the three months ended March 31, 2013 and 2012 (in thousands, except per-share amounts).

|  | Three Months Ended March 31, |
|  | 2013 |  |  | 2012 |
Net (loss) income |  | $ | (347 | ) |  | $ | 1,714 |
Adjustments for certain items: |  |  |  |  |  |  |  |
Unrealized loss on commodity derivatives |  |  | 4,100 |  |  |  | 2,672 |
Related income tax effect |  |  | (1,394 | ) |  |  | (908 | )
Adjusted net income |  | $ | 2,359 |  |  | $ | 3,478 |
Adjusted net income per diluted share |  | $ | 0.06 |  |  | $ | 0.10 |

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EBITDAX

We define EBITDAX as net (loss) income, plus (1) exploration expense, (2) depletion, depreciation and amortization expense, (3) share-based compensation expense, (4) unrealized loss on commodity derivatives, (5) interest expense, and (6) income taxes. EBITDAX is not a measure of net income or cash flow as determined by GAAP. The amounts included in the calculation of EBITDAX were computed in accordance with GAAP. EBITDAX is presented herein and reconciled to the GAAP measure of net income because of its wide acceptance by the investment community as a financial indicator of a company’s ability to internally fund development and exploration activities. This measure is provided in addition to, and not as an alternative for, and should be read in conjunction with, the information contained in our financial statements prepared in accordance with GAAP (including the notes), included in our SEC filings and posted on our website.

The table below provides a reconciliation of EBITDAX to net (loss) income for the three months ended March 31, 2013 and 2012, respectively (in thousands, except per-share amounts).

|  | Three Months Ended March 31, |
|  | 2013 |  |  | 2012 |
Net (loss) income |  | $ | (347 | ) |  | $ | 1,714 |
Exploration |  |  | 260 |  |  |  | 1,287 |
Depletion, depreciation and amortization |  |  | 17,056 |  |  |  | 11,030 |
Share-based compensation |  |  | 2,257 |  |  |  | 2,232 |
Unrealized loss on commodity derivatives |  |  | 4,100 |  |  |  | 2,672 |
Interest expense, net |  |  | 1,229 |  |  |  | 887 |
Income tax (benefit) provision |  |  | (187 | ) |  |  | 982 |
EBITDAX |  | $ | 24,368 |  |  | $ | 20,804 |
EBITDAX per diluted share |  | $ | 0.63 |  |  | $ | 0.62 |

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Liquidity

Liquidity is calculated by adding the net funds available under our revolving credit facility and cash and cash equivalents. We use liquidity as an indicator of the Company’s ability to fund development and exploration activities. However, this measurement has limitations. This measurement can vary from year-to-year for the Company and can vary among companies based on what is or is not included in the measurement on a company’s financial statements. This measurement is provided in addition to, and not as an alternative for, and should be read in conjunction with, the information contained in our financial statements prepared in accordance with GAAP (including the notes), included in our SEC filings and posted on our website.

The table below summarizes our liquidity at March 31, 2013, and our liquidity at March 31, 2013, on a pro forma basis to give effect to our May 1, 2013, borrowing base increase (in thousands).

|  | Liquidity at March 31, 2013 |  |  | Liquidity Pro Forma for Borrowing Base Increase at March 31, 2013 |
Borrowing base |  | $ | 280,000 |  |  | $ | 315,000 |
Cash and cash equivalents |  |  | 594 |  |  |  | 594 |
Outstanding letters of credit |  |  | (325 | ) |  |  | (325 | )
Long-term debt |  |  | (152,250 | ) |  |  | (152,250 | )
Liquidity |  | $ | 128,019 |  |  | $ | 163,019 |

Long-Term Debt-to-Capital

Long-term debt-to-capital ratio is calculated as of March 31, 2013, and by dividing long-term debt (GAAP) by the sum of total stockholders’ equity (GAAP) and long-term debt (GAAP). We use the long-term debt-to-capital ratio as a measurement of our overall financial leverage. However, this ratio has limitations. This ratio can vary from year-to-year for the Company and can vary among companies based on what is or is not included in the ratio on a company’s financial statements. This ratio is provided in addition to, and not as an alternative for, and should be read in conjunction with, the information contained in our financial statements prepared in accordance with GAAP (including the notes), included in our SEC filings and posted on our website.

The table below summarizes our long-term debt-to-capital ratio at March 31, 2013 and December 31, 2012 (in thousands).

|  | March 31, 2013 |  |  | December 31, 2012 |
Long-term debt |  | $ | 152,250 |  |  | $ | 106,000 |
Total stockholders’ equity |  |  | 635,211 |  |  |  | 633,468 |
|  | $ | 787,461 |  |  | $ | 739,468 |
Long-term debt-to-capital |  |  | 19.3 | % |  |  | 14.3 | %