The specific contact resistance rho(c) of ohmic contacts to semiconductors can be measured in a number of ways. In this paper the circular transmission line model by Reeves [Reeves GK. Specific contact resistance using a circular transmission line model. Solid-State Electronics 1980;23:487-490] is refined. It is expanded for the case that the resistivity of the metal contacts can not be neglected. The necessity of this expansion is evident, if more than just three contact rings are used. Since Reeves used only three contacts, he was not able to see the influence of the metal layer resistivity. Applying his model unchanged to a contact pattern with several rings, reveals that rho(c) changes systematically from the innermost pair of rings to the outermost pair. The refined model, which is presented here, accounts for this and allows to compute an unambiguous value for rho(c).