The Gas-Assisted Injection Moulding process (GAIM) offers a number of advantages, which are almost without exception related to the negligible pressure drop in the gas core of the moulded product. Accurate prediction of the gas distribution inside GAIM products is, however, still a major problem to be solved. As gas penetration is governed by three-dimensional phenomena, one has to resort to numerical simulations to analyse the process. Therefore, a numerical model for GAIM simulations has been developed, based on a physical, rather than on an empirical approach. The model employs a pseudo-concentration method in order to avoid elaborate three-dimensional remeshing, and has been implemented in a finite element program. Simulation results for two-dimensional test cases representing typical GAIM situations prove that the model covers most of the important aspects of gas injection. A pilot simulation for a simple three-dimensional mould demonstrates that the model is able to deal with three-dimensional GAIM. Further refinement of the model will mainly concern the implementation of faster and less memory-consuming solution methods.