An analytical elastic-plastic stress analysis is carried out in a low density polyethylene thermoplastic composite beams supported from two ends under a transverse uniformly distributed load reinforced by Cr-Ni steel fibers analytically. In the elasto-plastic solution, the material is assumed to be perfectly plastic. The intensity of the uniform force is chosen as a small value; therefore, the normal stress component of sigma(y) is neglected during the elasto-plastic solution. The expansion of the plastic region and the residual stress component of sigma(x) are determined for 0, 30, 45, 60 and 90degrees orientation angles. The intensity of residual stress component of sigma(x) is maximum at the upper and lower surfaces, but residual stress component of tau(xy) is maximum on the x axis of the beam. Plastic yielding occurs for 0 and 90degrees orientation angles on the lower and upper surfaces of the beam at the same distances from the mid point. However, it starts first at the lower surface for 30, 45 and 60degrees orientation angles.