NiTi shape memory alloy has many engineering applications including in bio-medical devices and implants, aerospace structures and micro-electro-mechanical systems due to its unique super-elasticity, shape memory effect and good biological compatibility. These structure components are often subjected to a kind of cyclic loading including pure mechanical and thermo-mechanical cyclic loading due to their special engineering applications. A stress-induced martensitic transformation and its reverse transformation will occur in the super-elastic NiTi alloy under the cyclic tension-unloading tests; while a martensite re-orientation will take place in the shape-memory NiTi alloy during the cyclic tension-unloading tests. With the increase in the number of cycles, the material parameters and the transformation behaviors will also change. However, the referable results are mainly obtained under the strain-controlled cyclic loading rather than the stress-controled cyclic. In order to improve the design of shape memory alloy components and to assess their reliability, it is necessary to carry out the study on the deformation behaviors of the NiTi shape memory alloy under the stress-controled cyclic loading. Moreover, it is also important to establish a constitutive model to describe the cyclic deformation behavior of NiTi shape-memory alloy.This thesis is mainly concerned with the following studies:(1) Super-elastic NiTi alloy was experimentally observed by the tension-unloading tests with peak stresses of 450MPa, 500MPa and 550MPa. The stress-strain curves, nominal elastic modulus of austenite, peak strain, valley strain and dissipation energy were discussed.(2) Shape memory NiTi alloy was also the experimentally observed by the tension-unloading tests study with peak stress of 240MPa, 470MPa, 600MPa and 700MPa. The stress-strain curves, peak strain, valley strain and dissipation energy were discussed.(3)A new constitutive model describing the transformation ratcheting of super-elastic NiTi alloy is proposed. The capability of the proposed model to predict the transformation ratchetting of the NiTi alloy was verified by comparing the simulated results with the corresponding experimental ones.