NiTi shape memory alloy (SMA) vascular stent, with good bio-compatibility and super-elastic properties, has become an important medical device in clinical treatment of cardiovascular or cerebrovascular diseases. The free expansion of stent in vessel involves the mechanical behavior of geometric large deformation related to the structure of super-elastic. In this paper, the nonlinear mechanical model for the substructure of NiTi shape memory alloy vascular stent is established, and the displacement deformation equation is derived. The geometric non-linearity of the structure is proved. Furthermore, the geometric nonlinear mechanical model is verified by numerical method. The mechanical analysis model of NiTi shape memory alloy vascular stent is widely used in the field of tracheal stent and so on.