<SEC-DOCUMENT>0001140361-13-032028.txt : 20130813
<SEC-HEADER>0001140361-13-032028.hdr.sgml : 20130813
<ACCEPTANCE-DATETIME>20130813154134
ACCESSION NUMBER:		0001140361-13-032028
CONFORMED SUBMISSION TYPE:	4
PUBLIC DOCUMENT COUNT:		1
CONFORMED PERIOD OF REPORT:	20130812
FILED AS OF DATE:		20130813
DATE AS OF CHANGE:		20130813

ISSUER:		

	COMPANY DATA:	
		COMPANY CONFORMED NAME:			Seneca Foods Corp
		CENTRAL INDEX KEY:			0000088948
		STANDARD INDUSTRIAL CLASSIFICATION:	CANNED, FRUITS, VEG & PRESERVES, JAMS & JELLIES [2033]
		IRS NUMBER:				160733425
		STATE OF INCORPORATION:			NY
		FISCAL YEAR END:			0331

	BUSINESS ADDRESS:	
		STREET 1:		3736 SOUTH MAIN STREET
		CITY:			MARION
		STATE:			NY
		ZIP:			14505
		BUSINESS PHONE:		315 926 8100

	MAIL ADDRESS:	
		STREET 1:		3736 SOUTH MAIN STREET
		CITY:			MARION
		STATE:			NY
		ZIP:			14505

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	SENECA FOODS CORP /NY/
		DATE OF NAME CHANGE:	19920703

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	PIERCE S S COMPANY INC
		DATE OF NAME CHANGE:	19861210

	FORMER COMPANY:	
		FORMER CONFORMED NAME:	SENECA FOODS CORP
		DATE OF NAME CHANGE:	19780425

REPORTING-OWNER:	

	OWNER DATA:	
		COMPANY CONFORMED NAME:			Exner John David
		CENTRAL INDEX KEY:			0001348503

	FILING VALUES:
		FORM TYPE:		4
		SEC ACT:		1934 Act
		SEC FILE NUMBER:	000-01989
		FILM NUMBER:		131032969

	MAIL ADDRESS:	
		STREET 1:		3736 SOUTH MAIN STREET
		CITY:			MARION
		STATE:			NY
		ZIP:			14505
</SEC-HEADER>
<DOCUMENT>
<TYPE>4
<SEQUENCE>1
<FILENAME>doc1.xml
<DESCRIPTION>FORM 4
<TEXT>
<XML>
<?xml version="1.0"?>
<ownershipDocument>

    <schemaVersion>X0306</schemaVersion>

    <documentType>4</documentType>

    <periodOfReport>2013-08-12</periodOfReport>

    <notSubjectToSection16>0</notSubjectToSection16>

    <issuer>
        <issuerCik>0000088948</issuerCik>
        <issuerName>Seneca Foods Corp</issuerName>
        <issuerTradingSymbol>SENEA</issuerTradingSymbol>
    </issuer>

    <reportingOwner>
        <reportingOwnerId>
            <rptOwnerCik>0001348503</rptOwnerCik>
            <rptOwnerName>Exner John David</rptOwnerName>
        </reportingOwnerId>
        <reportingOwnerAddress>
            <rptOwnerStreet1>3736 SOUTH MAIN STREET</rptOwnerStreet1>
            <rptOwnerStreet2></rptOwnerStreet2>
            <rptOwnerCity>MARION</rptOwnerCity>
            <rptOwnerState>NY</rptOwnerState>
            <rptOwnerZipCode>14505</rptOwnerZipCode>
            <rptOwnerStateDescription></rptOwnerStateDescription>
        </reportingOwnerAddress>
        <reportingOwnerRelationship>
            <isDirector>0</isDirector>
            <isOfficer>1</isOfficer>
            <isTenPercentOwner>0</isTenPercentOwner>
            <isOther>0</isOther>
            <officerTitle>General Counsel &amp; Asst Sec'y</officerTitle>
            <otherText></otherText>
        </reportingOwnerRelationship>
    </reportingOwner>

    <nonDerivativeTable>
        <nonDerivativeTransaction>
            <securityTitle>
                <value>Seneca Foods Class A Common</value>
            </securityTitle>
            <transactionDate>
                <value>2013-08-12</value>
            </transactionDate>
            <deemedExecutionDate></deemedExecutionDate>
            <transactionCoding>
                <transactionFormType>4</transactionFormType>
                <transactionCode>A</transactionCode>
                <equitySwapInvolved>0</equitySwapInvolved>
            </transactionCoding>
            <transactionAmounts>
                <transactionShares>
                    <value>377</value>
                </transactionShares>
                <transactionPricePerShare>
                    <footnoteId id="F2"/>
                </transactionPricePerShare>
                <transactionAcquiredDisposedCode>
                    <value>A</value>
                </transactionAcquiredDisposedCode>
            </transactionAmounts>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>3505</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeTransaction>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Seneca Class A Common</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>633.1</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401-K Match</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Seneca Class B Common</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>122.2</value>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>I</value>
                </directOrIndirectOwnership>
                <natureOfOwnership>
                    <value>401-K Match</value>
                </natureOfOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
        <nonDerivativeHolding>
            <securityTitle>
                <value>Seneca Class B Common</value>
            </securityTitle>
            <postTransactionAmounts>
                <sharesOwnedFollowingTransaction>
                    <value>73</value>
                    <footnoteId id="F1"/>
                </sharesOwnedFollowingTransaction>
            </postTransactionAmounts>
            <ownershipNature>
                <directOrIndirectOwnership>
                    <value>D</value>
                </directOrIndirectOwnership>
            </ownershipNature>
        </nonDerivativeHolding>
    </nonDerivativeTable>

    <derivativeTable></derivativeTable>

    <footnotes>
        <footnote id="F1">These shares were acquired in lieu of cash compensation pursuant to the Company's Executive Profit Sharing Bonus Plan.</footnote>
        <footnote id="F2">Award of restricted stock pursuant to the Company's 2007 Equity Compensation Plan, which was approved by the shareholders of the Company on August 10, 2007.  No price was paid by the Reporting person in connection with this award of shares of restricted stock which vests 25% per year over the next four years.</footnote>
    </footnotes>

    <remarks></remarks>

    <ownerSignature>
        <signatureName>Jeffrey L. Van Riper, As Attorney in Fact</signatureName>
        <signatureDate>2013-08-13</signatureDate>
    </ownerSignature>
</ownershipDocument>
</XML>
</TEXT>
</DOCUMENT>
</SEC-DOCUMENT>
