A mortar is a composite of inert sand grains surrounded by a porous cement paste matrix. We investigate the electrical conductivity of model mortars that include enhanced electrical conduction in the matrix–sand grain interfacial region. The electrical conductivity is evaluated by a combination of finite element, finite difference, and random walk methods for periodic and disordered models of mortar. Since the effective conductivity within the interfacial zone is often much higher than the bulk matrix conductivity, the qualitative features of transport in these systems is often controlled by the connectivity of the interfacial zone. Special attention is thus given to the geometrical percolation of this zone. A family of effective medium approximations give a good qualitative description of the disordered model’s electrical properties. A simple four parameter Pade´ approximant is found to successfully describe the electrical conductivity of the periodic model over the entire range of parameters studied. Finally, we show that our calculations can be used to obtain a reasonable estimate of the permeability to viscous fluid flow. ©1995 American Institute of Physics.