ABSTRACT We present an analytical model that describes the response of companion stars after being impacted by a supernova in a close binary system. This model captures key properties of the luminosity evolution obtained from 1D stellar evolution calculations fairly well: a high-luminosity plateau phase and a decaying tail phase. It can be used to constrain the pre-supernova binary properties from the observed photometry of the companion star several years after the explosion in a relatively simple manner. The derived binary parameters are useful in constraining the evolutionary scenario for the progenitors and the physics of binary interactions. We apply our model to some known stripped-envelope supernova companions (SN1993J, SN2001ig, SN2006jc, SN2011dh, and SN2013ge). Combined with other observational constraints such as the pre-supernova progenitor photometry, we find that SN1993J and SN2011dh likely had relatively massive companions on wide orbits, while SN2006jc may have had a relatively low-mass companion on a tight orbit. This trend suggests that Type IIb supernova progenitors evolved from stable mass transfer channels and Type Ibc progenitors may have formed from common-envelope channels. The constraints on orbital separation helps us probe the highly uncertain common-envelope physics for massive stars, especially with multiple epochs of companion observations. We also highlight possible limitations of our model due to the assumptions made in the underlying 1D models.