Acoustic cavitation, which is bubble growth and collapse in a liquid containing pre-existing gas nuclei by ultrasound irradiation, is an important topic in various medical and environmental applications including drug delivery and water treatment. A fundamental understanding and prediction of the bubble motion and associated tissue deformation is essentially important for its practical applications. In this work, a numerical approach is presented for acoustic cavitation and tissue deformation. A level-set method is used to track multiple bubble and tissue surfaces and is extended to compressible multiphase flows with phase change due to heat and mass transfer. The level-set method is further extended to include tissue deformation by combining with a full Eulerian formulation of a left Cauchy-Green deformation tensor for viscoelastic neo-Hookean materials. The numerical results demonstrate that the air-vapor mixture bubble growing in an acoustic field, following non-spherical contraction and rapid collapse, induces a strong shock wave and liquid jet penetrating the bubble, which causes deformation on the nearby tissue surface. The effects of acoustic parameters and tissue properties on the bubble motion and tissue deformation are further investigated.