Analytical procedures are developed for a composite system consisting of shape memory alloy fibers within an elastic matrix subject to uniform temperature. A three-phase concentric cylinder model is developed for the analysis of local stresses, which includes the fiber, the matrix, and the surrounding homogenized composite. The solution addresses the complexities induced by the nonlinear dependence of the in situ martensite fraction of the fibers on the local stresses and temperature and the local stresses developed from interactions between the fibers and matrix during the martensitic and reverse phase transformations. Results are presented for a Ni-44.8wt% Ti/epoxy composite. The applications illustrate the response of the composite in isothermal longitudinal loading and unloading. The local stresses developed in the composite under various stages of the martensitic and reverse phase transformations are also shown.