Strongly correlated metal strontium vanadate (SrVO3) was recently proposed to be used as a promising transparent conductor. Control of the optical and electrical properties of SrVO3 thin films using external stimuli is highly desired for most practical applications. Herein, flexible heteroepitaxial SrVO3 films on mica substrates were synthesized in a simple process using a pulsed laser deposition (PLD) method, showing high optical transparency and excellent electrical conductivity. The experiments demonstrate that the resistivity of flexible SrVO3 films depends strongly on the applied mechanical strain whereas the optical transmittance is retained during the bending tests. It is shown that two distinctly different resistivity values are switched back and forth repeatedly upon applying or removing a mechanical bending strain. The measured resistivity increases with increasing mechanical strain, which is attributed to the enhanced residual resistivity present in flexible SrVO3/mica membranes upon the application of a mechanical strain. We demonstrate that mechanical strain allows effective tuning of electrical conductivity in epitaxial SrVO3/mica membranes. The transparent conducting oxide SrVO3/mica membranes with highly tunable electrical conductivity show great potential for future flexible electronics and photovoltaics.