A triaxial failure criterion has been applied together with the theory of plasticity to model the behaviour of concrete subjected to compressive impact loads. The behaviour of concrete under the action of compressive stresses has been simulated using elastic-plastic fracture formulations. Under tension, an elastic stress-strain relationship has been used together with a smeared cracking model, tension softening and for the retained stresses a shear retention model. Failure of the concrete is either by cracking or crushing depending on the value of crushing coefficient determined as a function of the triaxial stress conditions. Verification of the analytical procedure has been undertaken by comparing the results with those obtained from published laboratory based investigations. It has been found that by using the above approach, the behaviour of concrete can be predicted to a reasonable degree of accuracy. The stress at or near failure can be calculated using the above formulation. The propagation of the cracks and the modes of failure can also be determined using the proposed concrete model.