An analytical elastic-plastic stress analysis is carried out on thermoplastic composite beams supported from two ends under transverse uniformly distributed load. The composite beams consist of woven steel fiber and thermoplastic matrix. The material is assumed to be perfectly plastic for the elastic-plastic solution. The intensity of the uniform force is chosen at a small value; therefore the normal stress components of sigma(y), is neglected during the elastic-plastic solution. The expansion of the plastic region and the residual stress component of sigma(x) are determined for 0degrees, 15degrees, 30 and 45degrees orientation angles. Plastic yielding occurs first 0degrees and 45degrees orientation angles on the lower and upper surfaces of the beam at the same distances from the ends. However; it starts first at the lower surface for 15degrees, 3degrees orientation angles. The intensity of the residual stress component of sigma(x) is found to be maximum at the lower and upper surfaces; whereas the intensity of residual stress component tau(xy) is maximum on or around the x axis of the beam.