In this work, an elastic-plastic stress analysis has been conducted for silicon carbide fiber reinforced magnesium metal matrix composite beam. The composite beam has a rectangular cross section. The beam is cantilevered and is loaded by a single force at its free end. In solution, the composite beam is assumed perfectly plastic to simplify the investigation. An analytical solution is presented for the elastic-plastic regions. In order to verify the analytic solution results were compared with the finite element method. An rectangular element with nine nodes has been choosen. Composite plate is meshed into 48 elements and 228 nodes with simply supported and in-plane loading condations. Predictions of the stress distributions of the beam using finite elements were overall in good agreement with analytic values. Stress distributions of the composite beam are calculated with respect to its fiber orientation. Orientation angles of the fiber are chosen as $0^{circ},;30^{circ},;45^{circ},;60^{circ};and;90^{circ}$. The plastic zone expands more at the upper side of the composite beam than at the lower side for $30^{circ},;45^{circ};and;60^{circ}$ orientation angles. Residual stress components of ${sigma}_{x};and ;{ au}_{xy}$ are also found in the section of the composite beam.