We present a theoretical study of the influence of the misfit strain on the transverse magnetooptic Kerr effect (TMOKE) and the transverse shift (Imbert–Fedorov effect) experienced by a light beam reflected from the surface of a magnetic/non-magnetic bilayer. The bilayer consists of a magnetic, gyrotropic yttrium-iron garnet film epitaxially grown on a non-magnetic dielectric gadolinium-gallium garnet slab. We use Green’s function method to calculate the reflection matrix in the presence of strain. It is shown that the mechanical strain present in the vicinity of the geometrical interface between the constituents of the bilayer can induce a non-negligible contribution to the TMOKE and the Imbert–Fedorov shift (IFS) for incidence angles close to those satisfying the half-wave condition for both layers, at which neither the TMOKE nor the transverse shift would appear in the absence of strain. We analyze the dependence of the IFS on the state of polarization of the incident