Oscillating microbubbles within microvessels could induce stresses that lead to bioeffects or vascular damage. Previous work has attributed vascular damage to the vessel expansion or bubble jet. However, ultra-high speed images of recent studies suggest that it could happen due to the vascular invagination. Numerical simulations of confined bubbles could provide insight into understanding the mechanism behind bubble-vessel interactions. In this study, a finite element model of a coupled bubble/fluid/vessel system was developed and validated with experimental data. Also, for a more realistic study viscoelastic properties of microvessels were assessed and incorporated into this comprehensive numerical model. The wall shear stress (WSS) and circumferential stress (CS), metrics of vascular damage, were calculated from these simulations. Resultant amplitudes of oscillation were within 15% of those measured in experiments (four cases). Among the experimental cases, it was numerically found that maximum WSS values were between 1.1-18.3 kPa during bubble expansion and 1.5-74 kPa during bubble collapse. CS was between 0.43-2.2 MPa during expansion and 0.44-6 MPa while invaginated. This finding confirmed that vascular damage could occur during vascular invaginations. Predicted thresholds in which these stresses are higher during vessel invagination were calculated from simulations.