In this book, we present numerical and data-driven methods for the modeling ofmultiphase physics involving cavitating bubble dynamics in and near elastic andviscoelastic materials. In the first part, we make use of data assimilation withbubbles cavitating in a viscoelastic hydrogel to estimate its mechanical properties.This method to characterize soft materials can aid in the modeling of biomaterialsin settings where high strain rates occur. In the second part, we implement anumerical framework for the direct numerical simulation of acoustic wave-bubble-stone interactions. This is used to simulate burst-wave lithotripsy, a treatment tobreak kidney stones through exposure to repeated bursts of focused ultrasound. Inparticular, this framework enables a better understanding of the impact and dynamicsof bubbles that can form near the stone during treatment.