Polymer-matrix composite beam of arbitrary orientation supported from two ends acted upon with a force at the mid point is studied by an analytical elasto-plastic stress analysis. In the elasto-plastic solution, the material is assumed to be perfectly plastic. 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 yielding begins for 0 and 90degrees orientation angles at the upper and lower surfaces of the beam at the same distances from the mid point. But, it starts first at the lower surface for 30, 45 and 60degrees orientation angles. The intensity of the residual stress component of tau(xy) is maximum on or around the x axis of the beam but the residual stress component of sigma(x) is maximum at the upper and lower surfaces. The beam can be strengthened by using the residual stress.