Advanced polymer matrix composites exhibit time-dependent deformation and fracture owing to the viscoelastic nature of the polymer matrix. Often this rate dependency is characterized under a single loading mode while the material is simultaneously subjected to multiple loading modes while in service. While the former has been extensively studied, the published research on the latter is very limited. Hence, in the present work, a criterion to predict strain-rate dependent failure of unidirectional continuous carbon fiber polymer matrix composite (Hexcel’s G30-500/F263-7), under multi-axial loading is developed by combining the critical stored elastic energy criterion developed by Raghavan and Meshi [1, 2] for predicting rate-dependent failure under uni-axial loading and Sandhu’s criterion for predicting rate-independent failure for multi-axial loading [3]. Strain-rate dependent critical stored energy for on-axis loading (longitudinal normal, transverse normal, and shear) were determined using the procedure developed by Raghavan and Meshii [1, 2] and tensile testing of [0], [90], and V-notched rail shear test specimens respectively, at three strain rates (10 pwr -3, 10 pwr -4 and 10 pwr -5 per sec), and at various temperatures (24, 80, 120, 160, 200, 245 and 275 C). Using this along with the modified Sandhu’s criterion, the tensile strength of off-axis laminates (10, 15, 30, 45, 60, and 75 degrees), at the strain rates and temperatures identified above, were predicted and compared with the experimental results. Furthermore, the results were plotted as failure envelope in the first stress quadrant (shear stress (τ12) versus tensile transverse normal stress (σ22)) and evaluated. The failure criterion developed in this study resulted in predictions with accuracy (within 8% of experimental results at all strain rates and temperatures) much better than predictions using Tsai-Hill, Hashin-Rotem, and Sandhu’s failure criteria.