Segmented polyurethane (PU) polymers are known to have shape memory function, i.e., when they reach certain temperatures, they deform into the memorized shape from any temporary one. In the present study, PU polymers were spun into fibers using the conventional extrusion process to investigate the feasibility of producing smart fibers with shape memory function. The shape memory polymers (SMPs) and their spun fibers were characterized using DSC, DMTA, and tensile test. In particular, the thermo-mechanical deformation behavior, which enables to evaluate the shape memory performance of the SMPs, was characterized using DMTA. Then, the linear viscoelastic theory was utilized for mathematical modelling of the thermo-mechanical behavior of the SMPs. For the shape memory fibers, the large deformation characteristics were also investigated using the thermo-mechanical test, necessitating the development of nonlinear viscoelastic theory to formulate a constitutive equation and to provide an effective tool for designing smart textile structure.