Stent sizing and apposition have been shown to be important determinants of clinical outcome. This study evaluates the mechanical effects of under-sizing and over-sizing of stents on endothelial wall shear stress (WSS) and vessel wall stress to determine a possible biomechanical mechanism of in-stent restenosis and thrombosis. Three-Dimensional computational models of stents, artery and internal fluid were created in a computer assisted design package, meshed and solved in finite element and computational fluid dynamic packages. The simulation results show that the effects of various degrees of under-sizing on WSS, WSS gradient (WSSG) and oscillatory shear index (OSI) were highly non-linear. As the degree of under-sizing increased, the heterogeneity of WSS became smaller. The WSS distribution for the 20% under-sizing was smooth and uniform, whereas the 5% case was very heterogeneous. The combination of lower WSS and higher WSSG and OSI in the 5% under-sized case may induce neointimal hyperplasia or thrombosis. Additionally, the over-sizing simulation results show that the maximum intramural wall stress of the 20% over-sizing case is significantly larger than the maximum stress for the 10% and zero over-sizing cases. Edge stress concentration was observed, consistent with the re-stenosis typically observed in this region. This study demonstrates that proper sizing of stent is important for reducing the hemodynamic and mechanical disturbances to the vessel wall. Furthermore, the present findings may be used to improve stent design to reduce endothelial flow disturbances and intramural wall stress concentrations.