Beams are structural elements loaded transversely in general conditions. This loading causes shear forces and bending moment. In this study, an analytical elastoplastic stress analysis is carried out on simply supported stainless steel fiber-reinforced aluminum alloy metal-matrix composite beams under linearly distributed load by use of anisotropic elasticity theory. In the elastoplastic solution, the material is assumed to be perfectly plastic. Sample problems are given for various angles analytically. The yielding begins at the upper and lower surfaces of the beam at the same distances from the ends. The intensity of residual stress component of sigma(x) is a maximum at the upper and lower surfaces whereas the residual stress component of tau(xy) is maximum on the x axis of the beam. The composite beams can be strengthened by using the residual stresses.