An analysis for failure prediction is presented for laminated composites under extension and bending. The method is based on the determination of the fiber and matrix strains in each composite lamina. Under combined extension and bending, layer strains in a composite section are computed by means of the laminate theory and used as input for a three dimensional elasticity analysis to calculate fiber and matrix strains in each lamina of the composite section. Maximum principal strain failure criterion is applied to fiber and matrix separately. Two dimensional failure envelopes based on failure initiation and first ply failure of combined loading cases are presented and compared with the results of Tsai-Wu failure criterion.