The influence of various strains on the crystal and electronic structures of superconducting FeSe has been studied ab initio. We consider changes in the Fermi surface nesting with a vector Q = (0.5, 0.5) x (2 pi/a) as crucial for rising superconductivity (SC) mediated by spin fluctuations (SF). Our results indicate that the c-axis-strained FeSe exhibits the most imperfect nesting, which enhances SF and, hence, also SC. In turn, the ab-plane compressive strain slightly weakens this nesting while the tensile strain destroys it completely. These findings are consistent with earlier reported experimental dependences of the superconducting transition temperatures on strain in FeSe thin films. Copyright (C) EPLA, 2012