Mechanochemical transduction plays a vital role in biological processes. There have, however, been few studies on exploiting mechanical stimuli to trigger chemical signals in non-biological systems. Using computational modeling, we investigate how an applied mechanical pressure can be harnessed to initiate traveling chemical waves in polymer gels undergoing the Belousov–Zhabotinsky (BZ) reaction. We uncover a rich dynamic behavior, isolating systems where the applied pressure induces chemical oscillations in an initially non-oscillatory system. We also pinpoint a scenario where the compression induces both oscillations and the autonomous rotation of the entire sample. Determining factors that control mechanochemical transduction in BZ gels is necessary for establishing guidelines to create self-adjusting or adaptive materials that not only “sense” a localized impact, but also transmit a global chemical signal in response to the local mechanical perturbation. Such materials can potentially be used to fabricate touch-sensitive sensors and membranes, as well as self-reinforcing materials.