An analytical potential calculation strategy is worked out, using the analytical solution of Laplace’s equation in cylindrical and toroidal configurations with rectangular sectional shape and rotation symmetrical boundary conditions. This strategy makes it possible to calculate the potential distribution to any desired rate of accuracy, even in very complex rotation symmetrical lens systems, and serves as a basis for the calculation of charged particle trajectories. These calculations only have to be done in places or areas where the shapes of the particle trajectories are of interest, while only and in a direct way the potential distribution on the boundaries of the potential volume is used in the calculations. Even in regard to the commonly used charge density method, this analytical calculation procedure saves a great amount of computer memory and calculation time, since no matrix inversions are required anymore.