A type of excitable medium—an elastic excitable medium—has been created by incorporating the Belousov-Zhabotinsky reaction into a polyacrylamide-silica gel. It permits one to address the problem of how the cardiac muscle contractions affect the dynamics of rotating spiral waves. Investigations of the effects of mechanical deformations on the excitation wave propagation exhibit a resonance dynamics of vortices. For equal frequencies of deformation and of vortex rotation, vortices drift. The drift velocity is about 3% of the excitation wave velocity, for a 50% elongation. The direction of the drift does not coincide with the stretching direction and can be varied by changing the phase shift between deformations and vortex rotation. Numerical calculations suggest that the effects of mechanical deformations on excitation wave propagation are independent of the exact nature of the excitable medium.