An elasto-plastic stress analysis is carried out in a low density polyethylene thermoplastic cantilever beam of arbitrary orientation subjected to transverse linearly distributed load reinforced by Cr-Ni steel fibers analytically. 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 0degrees, 30degrees, 45degrees, 60degrees and 90degrees orientation angles. The yielding begins at the upper and lower surfaces of the beam at the same distances from the free end. 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, Sample problems are given for various angles,x axis of the beam is used to obtain the location of the clasto-plastic boundary and to Calculate elastic, elasto-plastic and residual normal and shear stresses.