<?xml version="1.0" encoding="UTF-8"?>

<!--XBRL Document Created with Wdesk from Workiva-->
<!--Copyright 2020 Workiva-->
<!--r:d1e36350-3529-4ca7-ae41-7acc1b9729c4,g:2ed41a07-84cb-4d47-8b49-2fb2bc8ddc51-->
<link:linkbase xmlns:link="http://www.xbrl.org/2003/linkbase" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://www.xbrl.org/2003/linkbase http://www.xbrl.org/2003/xbrl-linkbase-2003-12-31.xsd">
  <link:roleRef roleURI="http://www.fibk.com/role/Cover" xlink:type="simple" xlink:href="fibk-20200728.xsd#Cover"/>
  <link:calculationLink xlink:role="http://www.fibk.com/role/Cover" xlink:type="extended"/>
</link:linkbase>
