Inverse solution techniques based on electroencephalograph (EEG) measurements have become a powerful means of gaining knowledge about the functioning of the brain. A model of the head and a potential computation method are necessary to describe the EEG problem mathematically. The generation of realistically shaped three-compartment models of the head is discussed. The isolated problem approach for the boundary element method is applied to develop a fast and accurate numerical solution of the EEG forward problem. Accuracy studies with this approach show that dipole positions can be reconstructed within a distance of 3 mm from the original positions. Inverse simulations indicate that the incorporation of the individual head shape may significantly influence the reconstructed dipole position but not its magnitude and orientation, in comparison with the commonly used three-sphere model. However, the presence of noise in the simulated potential data affects the solutions based on realistically shaped models more than those of the simple three-sphere model. The increased censitivity of the former models to noise in the data remains a serious drawback for their practical application to EEG source localisations.