Abstract Noble's variational method is used to solve the contact resistance problem that arises when a circular disc source electrode is in contact with a semiconductor slab through an infinitesimally thin layer of resistive material. The method assumes that the source current density distribution J( r) has the form K 1(1 − r 2) −μ + K 2(1 − r 2) 1 2 + K 3(1 − r 2) 3 2 , where the parameters K 1, K 2, K 3 and μ are determined by variational principles. Calculations of the source current density and the total slab resistance, performed for a wide range of contact resistivities, show that the results are practically indistinguishable from those derived from an exact mixed boundary value method proposed earlier by us. Whilst this method of using an optimised μ is very accurate, it is computationally slow. By fixing μ at a constant value of 1 4 , we find that we can drastically reduce the computation time for each calculation of the total slab resistance to 1.5 s on an Apple II microcomputer, and still achieve an overall accuracy of 1%. Tables of the abscissas and weights required for implementation of the numerical scheme are provided in the paper.