The present study concerns the numerical modeling of microbubble oscillation within an elastic microvessel, aiming to enhance the safety and efficacy of ultrasound-mediated drug delivery and diagnostic imaging. The success of such applications depends on a thorough understanding of microbubble–vessel interactions. Despite some progress, the critical impact of the stabilizing shell around gas core has remained underexplored. To address this, we developed a novel numerical approach that models the stabilizing shell. Additionally, there is novelty in modeling consequent vascular deformation in response to complicated spatiotemporal microbubble oscillations. The novel approach was implemented for shear stress evaluation as a critical factor in vascular permeability. Finally, our unique approach offered novel insights into microbubble–vessel interactions under diverse acoustic conditions. Results indicated substantial impact of shell properties and acoustic parameters on induced shear stress. With a fourfold increase in acoustic pressure amplitude, 15.6-fold and sixfold increases were observed in maximum shear stress at 1 and 3 MHz, respectively. Also, the peak shear stress could reach up to 15.6 kPa for a shell elasticity of 0.2 N/m at 2.5 MHz. Furthermore, decreasing microvessel/bubble size ratio from 3 to 1.5 increased maximum shear stress from 5.1 to 24.3 kPa. These findings are crucial for optimizing ultrasound parameters in clinical applications, potentially improving treatment outcomes while minimizing risk of vessel damage. However, while our model demonstrated high fidelity in reproducing experimental observations, it is limited by assumptions of vessel geometry and homogeneity of vessel properties. Future work can improve our findings through in vitro experimental measurements.