In shape memory alloys (SMAs), the shape memory effect and superelastic characteristics appear owing to the martensitic transformation (MT). In practical applications of SMAs, they are subjected to various thermomechanical loadings. When an SMA is subjected to a mechanical load, especially at high strain rates, its temperature varies due to thermomechanical coupling in the response of these materials. In thermomechanical loadings, the mechanical loading/unloading and thermal heating/cooling processes in which the MT is completed are called full-loop loadings or complete-loop loadings. If the loading directions vary during the MT, before the MT is completed, the loading processes are called subloop loadings or internal loop loadings. Creep and stress relaxation are induced by the MT according to variations in temperature under subloop loadings. Thus, if strain is kept constant during the transformation, temperature change will cause stress to decrease during loading and to increase during unloading. A decrease in stress under constant strain indicates stress relaxation, and an increase in stress indicates stress recovery. Similarly, if stress is kept constant during the transformation, temperature change will cause strain to increase during loading and to decrease during unloading. An increase in strain under constant stress indicates creep, and a decrease in strain indicates creep recovery. In this thesis, a 1-D thermo-mechanical model is proposed and equations are extracted in continuum mechanics framework for stress-controlled and strain-controlled loadings to study stress relaxation and creep in SMA wires. Numerical analysis is done by developing a code in MATLAB. To study stress relaxation and creep in an SMA wire, three steps are considered: for stress relaxation, in the first step, strain-controlled loading at the specified strain rate is done up to a particular strain during transformation. In the second step, strain is kept constant and decrease in stress is seen indicating stress relaxation. In the last step, the applied strain is again increased at the same strain rate as the first step until the transformation is completed. Similarly, to study stress recovery, loading followed by incomplete unloading is first done. Then strain is kept constant leading to increase in the stress of an SMA wire. At last, unloading continues to the complete removal of the applied strain. For creep, firstly, stress-controlled loading is done up to a particular stress during transformation. In the second step, stress is kept constant and increase in strain is seen indicating creep. In the last step, the applied stress is again increased until the transformation is completed. In the same way, to study creep recovery, loading followed by incomplete unloading is first done. Then stress is kept constant leading to decrease in the strain. At last, unloading continues to the complete removal of the applied stress. Various relaxation and creep experiments were also performed on NiTi wires. For this aim, fabricating some equipment was required. Thus, the second part of this thesis corresponds to the manufacture of this equipment. Finally, various relaxation and creep experiments at different ambient temperatures and applied strain rates were done, and the empirical findings were found to coincide with the numerical results. The results indicate that increase in the applied strain rate as well as radius of an SMA wire gives rise to more pronounced stress relaxation and stress recovery. Moreover, increase in the applied strain rate and decrease in the radius of an SMA wire gives rise to more pronounced creep and creep recovery. Key Words Shape Memory Alloy Wire, Thermomechanical, Stress relaxation, Stress recovery, creep, creep recovery.