A spherical cavity expansion model for concrete is first proposed by using an elastic-brittle-plastic material law with Hoek-Brown strength criterion. The constitutive model can capture the basic features of the mechanical response of concrete materials including the effects of strain-softening and pressure hardening (pressure-dependent shear strength) and all the parameters used in the model can be determined from material tests. The forcing function obtained from the spherical cavity expansion analysis is then employed to construct a penetration model for concrete targets struck by ogival-nosed projectiles. It transpires that the present model predictions are in good agreement with experimental observations in terms of penetration depth and ballistic limits/residual velcoties in the case of perforation.