Inverse solution techniques based on electroencephalographic (EEG) measurements have become a powerful means to gain knowledge on 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 discnsed. The isolated-problem approach for the boundary element method (BEM) is applied to develop a fast and reliable 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 sigaxificantly 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. This effect is investigated more in detail by means of visualising the objective function of the dipole optimization. The locally optimal dipole is estimated in a dense grid o f scan points in the region of interest. This enables us to gain specific information about the steepness of the objective ftmcfion as well as about possible local minima caused by the realistically shaped head model or by rtoise in the EEG potentials.