The evolution of a bubble confined inside a nonlinear micro vessel fully filled with a viscous liquid, subjected to a shock lithotripsy wave (SWL), is analyzed with a previously established asymmetrical model on bubble oscillation. Both the normal and shear stress components within the vessel wall are calculated. It is observed that although the shear stress induced by viscosity is far less than the normal stresses, hypertension patients are still at more risk than normal people in SWL because of the high blood pre-pressure and stiff vessel wall accompanying their high blood viscosity. Hence, safety of hypertensive patients with high blood viscosity must be taken into careful consideration in SWL. More detailed numerical results show that the increase of circumferential normal stress and strain in SWL is significantly larger than that of other stresses and strains. Large circumferential normal stress and strain are responsible for excessive dilation of vessel wall during asymmetrical oscillation of constrained bubbles, which implies that the vessel wall will rupture mainly in the form of a cleft along the vessel axial direction.