An analytical elastic-plastic stress analysis is presented for a low density polyethylene thermoplastic composite reinforced by woven steel fibers supported at the ends acted upon with a force at the midpoint. The expansion of the plastic region and the residual stress component of sigma(x) are determined for theta = 0degrees, 15degrees, 30degrees and 45degrees orientation angles. Plastic yielding occurs for 0degrees and 45degrees orientation angles on the lower and upper surfaces of the beam at the same distances from the midpoint. But, it starts first at the lower surface for 15degrees and 30degrees orientation angles. The residual stress components are obtained after releasing the external force. The residual stress component of q, is maximum at the lower and upper surfaces. However, the intensity of the residual stress component tau(xy) is maxiumu on or around the x axis of the beam. The beam can be strengthened by using the residual stresses.