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This study details and demonstrates a strain-based criterion for the prediction of polymer matrix composite material damage and failure under shock loading conditions. Shock loading conditions are characterized by high-speed impacts or explosive events that result in very high pressures in the materials involved. These material pressures can reach hundreds of kbar and often exceed the material strengths by several orders of magnitude. Researchers have shown that under these high pressures, composites exhibit significant increases in stiffness and strength. In this work we summarize modifications to a previous stress based interactive failure criterion based on the model initially proposed by Hashin, to include strain dependence. The failure criterion is combined with the multi-constituent composite constitutive model (MCM) within a shock physics hydrocode. The constitutive model allows for decomposition of the composite stress and strain fields into the individual phase averaged constituent level stress and strain fields, which are then applied to the failure criterion. Numerical simulations of a metallic sphere impacting carbon/epoxy composite plates at velocities up to 1000 m/s are performed using both the stress and strain based criterion. These simulation results are compared to experimental tests to illustrate the advantages of a strain-based criterion in the shock environment.