A numerical method to solve Poisson's equation with an empirical set of boundary values gives potentials about complicated configurations such as occur in the lenses of electron microscopes. It involves solving an auxilliary induction problem and then solving the integral form of Poisson's equation numerically. The case for cylindrical symmetry has been coded on the IBM 7090 computer and a program developed that evaluates the electron optical properties of lenses possessing this symmetry.