Failure analysis of a laminated composite beam subjected to uniformly distributed load and thermal load is studied for different boundary conditions and fiber orientation angles, based on first ply failure load. Three different boundary conditions are studied: simply supported, fixed-fixed and fixed-free. The strength ratio is computed and compared for different failure theories. The effect of fiber orientation angle and aspect ratio on the strength ratio based on first ply failure load is presented in the paper. The strength ratio and transverse deflection are determined for Graphite/Epoxy and Glass/Epoxy composite and their hybrid combinations to find out the optimum hybrid composite beam with minimum weight, deflection and cost. The problem is solved in MATLAB platform. The mode of failure of the composite beam is determined by using maximum stress theory.