Ni-Ti alloy, one of well-known shape memory alloys, attracts attention by their functional advantages in thin films or their nanostructures. Stress induced martensitic transformation (SIMT) is recognized as a principal deformation mechanism, while its atomistic view on nucleation or prematensitic transformation is left unrevealed. Therefore, we computationally investigate microscopic mechanism of SIMT in Ni-Ti alloy using molecular dynamics simulation (MDS) with embedded atom metod (EAM) potential function. The Ni-Ti simulation model consisted of 19 404 atoms and surrounded by free surfaces is subjected to loading and unloading with appropriate structural relaxations. To identifying crystalline phase changes from B 2 (parent) to B 19' (martensite) in the alloy under loading, we monitor lattice parameters, ratio of two lattice parameters, and their angles from instantaneous atomic positions. We define the martensite phase by specifying possible combination of the parameters according to literatures. In loading process, with rapid stress descent, the MDS model deforms and shows maximal ratio of martensite phase. We find that there are two major paths of atomic configurational change from B 2 to B 19' in these martensite structures and there is also another kind of long-range atomic migration whose distance is larger than single lattice constant. The separation into these multiple paths is caused by discrepancy in angles between interatomic connecting line in unitcell and the tensile direction. It is also find that each paths have characteristic activation energies during configurational change (i.e. during phase transformation). It is ensured that SIMT is microscopically constructed by various types of structural changes and their energetics.