In biomedical sciences, numerical and modeling approaches to study biological systems often present significant challenges due to their multiscale nature and the interaction of various materials ranging from liquids and soft tissue to elastic solids. Many applications in the medical field involve the-often nonlinear-dynamical behavior of these materials in high strain-rate and/or high stress regimes. One example where such strain-rates and stresses are generated is during cavitation of single or clouds of bubbles. Treatments making use of focused ultrasound, shock waves, or laser surgery can cause nucleation of bubble clouds which collapse rapidly, deforming the surrounding material at high rates and inducing very high pressures at the bubble nucleation site. Understanding the interaction of such cavitating gas bubbles with viscoelastic materials and stiff elastic solids is thus valuable in various applications in the biomedical field.