Model based iterative reconstruction techniques (MOR) in Electrical Tomography have the potential to produce the most physically realistic reconstructed images. However the real-time performance of this method is presently constrained by the high computing requirements for the calculation of the “ forward problem” which utilises the finite element method. Most of the recent work towards a resolution of this computing problem has centered on the improvement of the computer hardware involved. However, our work has concentrated on improving the performance of the numerical algorithms. This paper demonstrates that a direct solution method for the finite element method can be utilised to determine the capacitance matrix of a multi-electrode sensor without recourse to intermediate potential field solutions. The paper discusses aspects of the finite element method which can influence the solution time and accuracy, and in particular the construction of an optimum mesh for particular multi-electrode problems. The mesh strategy and accuracy are compared with analytical models of the sensors constructed using conformal maps