A three-dimensional (3-D) Finite Element Analysis (FEA) model incorporating an elastic-plastic (EP) damage model, which was implemented as a user-defined material (‘VUMAT’) sub-routine in a FEA code (‘Abaqus/Explicit’), is developed to simulate the impact response of carbon-fibre reinforced-plastic (CFRP) composites. The model predicts the load versus time and the load versus displacement responses of the composite during the impact event. Further, it predicts the extent, shape and direction of any intralaminar damage and interlaminar delaminations, i.e. interlaminar cracking, as a function of the depth through the thickness of the impacted CFRP test specimen, as well as the extent of permanent indention caused by the impactor striking the composite plate. To validate the model, experimental results are obtained from relatively low-velocity impact tests on CFRP plates employing either a matrix of a thermoplastic polymer, i.e. poly(ether-ether ketone), or a thermosetting epoxy polymer. The 3-D EP model that has been developed is shown to model successfully the experimentally-measured impact behaviour of the CFRP composites.