A mathematical model for electromagnetic heating of oil shales is developed. The model includes equations for temperature, pressure, saturations, chemical reactions, mass conservation, and source terms. The gases are all assumed to form one bulk species and the oil is assumed to remain in liquid form. The chemical reactions include pyrolysis of kerogen and char, release of bound water, coking, and decomposition of carbonates. Porosity and permeability are dynamic functions of the shale constituents. Nonlinear relationships for viscosity, thermal properties, and source terms are used as inputs to the model. A finite difference approximation to the differential equations is derived and solved using Newton's iteration technique. For the cases studied the solutions are quite stable. Numerical results are included and a preliminary study of the optimization of the heating process is presented. 17 refs., 19 figs.