In this study, an elastic-plastic stress analysis is performed in a carbon fiber reinforced thermoplastic composite beam, which is loaded uniformly at the upper surface. An analytical solution is obtained including both the governing differential equations and boundary conditions. The composite beam is loaded uniformly at the upper surface, therefore the normal stress component σy is neglected in comparison with other stress components. The orientation angle of the composite is changed as 0°, 15°, 30° and 45°. The intensity of the residual stress component of σx is maximum at the upper and lower surfaces of the composite beam. The intensity of the residual stress component of the shear stress τxy is maximum around the central axis for the beam.