In this paper we present the mathematical foundations of the physical processes for true in-situ retorting by electromagnetic heating. The modeling of in-situ retorting via electromagnetic heating requires a mathematical formulation of the problem and empirical relations for such quantities as thermal conductivity, heat capacities, rate constants, permeabilities, and viscosities. The mathematical formulation consists of equations for conservation of species, saturations, capillary pressure, momentum and energy. These equations constitute a system of coupled nonlinear partial differential equations which must be solved numerically. The model has been run using various parameters. As an example we consider a well bored into the shale, a rf generator is inserted so that energy is emitted radially outward for the entire length of well bore. Because of cylindrical symmetry we need only model a slice in the r and z coordinates. Figures 3 to 5 show the contours of temperature at different times, figures 6 to 8 show the pressure at these times, figures 9 to 11 show the Kerogen concentration at these times in Kg/m/sup 3/, figures 12 to 14 show the coking, figures 15 to 17 show the carbon buildup and figures 18 to 23 show velocity profiles, and finally figure 24 shows the oil yield or a function of time in seconds. 8 references, 24 figures.