The numerical simulation of current and temperature distribution in monolithic solid oxide fuel cell (SOFC) stacks requires fast computers because of the large number of mesh points required in casting a complex solid geometry into a finite difference form and the necessity to solve coupled, nonlinear differential equations. By analogy with the modelling of radiative heat transfer in packed bed reactors, a significant degree of simplification is achieved by defining effective electric and thermal conductivities for the repeating unit cell elements, identified as the basic building blocks of the SOFC stack. The effective conductivities are approximated by closed form formulae derived from the principles of electrostatics and heat conduction. The effect of radiation across the gas channels is incorporated into the expressions for the effective thermal conductivity. Using this approach, the unit cell geometry, local mass transfer processes and reaction kinetics are expressed in terms of a supraelement model in a finite difference grid for the numerical calculation of temperature and potential distributions in a stack by an iterative process. The simplifications thus provided render simulations of three-dimensional SOFC stacks tractable for desktop processors. By using the foregoing approach to numerical simulation, a parametric study of a cross-flow type SOFC is presented, and some of the results are compared with the available experimental data.