Acoustic droplet vaporization (ADV) is a phenomenon in which volatile droplets are changed into bubbles by ultrasonic pulses. The ADV near a wall receives attention in medical applications such as ultrasound medical diagnosis and therapy. Despite a number of studies, a general predictive model for the ADV near deformable walls such as blood vessels has not yet developed due to the difficulties in tracking the multiple interfaces with phase change occurring in micro length and time scales. In this work, a level-set (LS) method is applied to ADV near a deformable wall to track the bubble-droplet and droplet-ambient liquid interfaces and to include droplet evaporation and bubble compressibility effects. The LS formulations for multiple fluid phases are extended to include solid deformation and fluid-solid interaction by incorporating a full Eulerian formulation of a left Cauchy-Green deformation for hyperelastic solid materials. Computations are performed for acoustic vaporization of dodecafluoropentane (DDFP) droplets with a low boiling point immersed liquid water at the human body temperature. The numerical results demonstrate the bubble growth and wall deformation in the whole ADV process of a DDFP droplet.