The implantation of an intravascular stent has become a widely used minimally invasive treatment for coronary heart disease due to its low invasiveness and high efficiency. But the long-term outcomes are often compromised by in-stent restenosis (ISR), which severely restricts its effectiveness in practical. In this paper, the formation mechanism of ISR was given, and the effects of mechanical environment on ISR were analyzed from the view of solid mechanics. The research progress of stent expansion in vessels with 4 different shapes, including straight vessel, tapered vessel, bifurcation vessel and curved vessel was reviewed. Moreover, the correlations between vessel stress and vessel shape change caused by stent expansion and ISR were reviewed. Finally, based on the influence of different vessel shapes on stent expansion, a multi-objective optimization design method was proposed to improve stent expansion performance and reduce the occurrence of ISR.