Based on the Timoshenko beam theory and the Tsai-Hill yield criterion, a mathematical model for elastic-plastic analysis for cantilever beams by bending moment was established. Meanwhile, the analytical solutions of stress and displacement were obtained. The solutions were verified in comparison with the ones available in the literature and finite element. Furthermore, the effects of fiber orientation angle, bending moment, aspect ratio and fiber volume fraction on the elastic-plastic stress and displacement of the beam were examined in detail. The results can provide important references for the design and engineering applications of thermoplastic composites.