In the present study, an elastic-plastic stress analysis is carried out on a composite thermoplastic disc reinforced by steel fibers, curvilinearly. Radial and tangential stresses are obtained under a liner temperature distribution. The magnitude of the tangential stress component for elastic and elastic-plastic cases is higher than that of the radial stress component. The tangential stress component is compressive and tensile on the inner and outer surfaces, respectively and is the highest on the inner surface. The elastic-plastic solution is performed for the plastic region expanded around the inner surface by an analytical formulation and a numerical solution. The solution is also carried out by the finite element method (ANSYS solution). These two solutions give very similar results. The intensities of the residual stress component of the tangential stress and plastic flow are the highest at the inner surface.