A micromechanical finite element model has been developed to investigate the failure of unidirectional  and 8-ply [0/0/90/90] s P75 Graphite/934 Epoxy composites subjected to mechanical and thermal loads based on the ultimate radial stress criterion developed by Bowles and Griffin. The ANSYS finite element program has been used to study the initiation of failure, the mode of failure and the applied stress at which the failure occurs, as well as the effect of thermal residual stresses on the failure of the composite material. Thermal residual stresses develop as a result of the differences in the coefficients of thermal expansion of the fiber and the matrix, and the operating and stress-free (or cure) temperatures. The results from the finite element analysis are compared to those obtained from the laminate plate theory. The finite element analysis and laminate plate theory predict the initial failure of the  plies in the [0/0/90/90]s composite material at an applied load of 46,400 and 86,000 lbs/in., respectively. Thermal residual stresses developed as a result of cool down from the cure temperature (350°F) to room temperature (75°F) are compressive at the fiber/matrix interface and thereby increase the failure stress as compared to materials with no thermal residual stresses. However, the mode of failure is different. The finite element analysis indicates intermediate degradation of the laminate as the applied stress is increased. This information is used to relate the loss in overall stiffness to the extent of failure at the fiber/matrix interface.