Modeling the dynamics of microbubbles inside confined spaces has many potential applications in biomedicine, sonoporation being one classic example. Sonoporation is the permeabilization of a blood vessel’s endothelial cell membrane by acoustic waves in order to non-invasively deliver large-sized drug molecules into cells for therapeutic applications. By controlled activation of ultrasound contrast agents (UCA) in a microvessel, one can achieve better permeabilization without causing permanent damage associated with high intensity ultrasound. This paper considers numerically, the fluid-structure interactions (FSI) of UCA microbubbles with a microvessel accounting for large deformations. The modeling approach is based on a multi-material compressible flow solver that uses a Lagrangian treatment for numerical discretization of cells containing an interface between two phases and an Eulerian treatment for cells away from material interfaces. A re-mapping procedure is employed to map the Lagrangian solution back to the Eulerian grid. The model is first validated by simulating a microbubble oscillating due to an imposed ultrasound inside a microvessel and good agreement with experiments is obtained for both the bubble and vessel dynamics. The effect of vessel elasticity is then studied and it is shown that increasing the vessel elasticity damps the bubble oscillations. Then the effect of placing the bubble away from the axis of vessel is studied and it is shown that bubbles closer the vessel wall are capable of creating maximum deformation on the wall compared to those away from the wall.