A theory is developed to model the dynamic of bubble and particle inside a spherical liquid-filled cavity surrounded by an elastic medium. The aim of this work is to study how the outer elastic medium affects the interaction between bubble and particle. Starting from the theory of velocity potential distribution, combined with Lagrangian equations, the motion equations of bubbles and particles in the cavity are obtained. The resonance frequency of the bubbles and influence of the interaction between particle and bubble on the translational behavior under the action of sound waves are analyzed. The results show that the properties of medium elasticity and density can change the resonance frequency of the bubble in the cavity. As the radius of the spherical cavity increases, the resonance frequency of the bubble has a tendency to first decrease and then increase, and gradually tends to the resonance frequency of a single bubble in an unbounded liquid. The translation of bubble and particle in the spherical liquid cavity is affected by factors such as acoustic field parameters, the characteristics of the outer elastic medium, and the characteristics of the bubble and particle themselves. The overall characteristic is that the particle has a tendency to move to the cavity wall, and the translation of bubble is closely related to the interaction characteristics between bubble and particle.