A mathematical model for the simulation of the transport phenomena occurred in the anode of a typical fuel cell is presented here. The model considers a planar two-dimensional geometry while the mass transport is described by the convection-diffusion equation within the catalyst under laminar flow conditions together with the kinetic and ohmic electrochemical effects. Convective heat transfer within the developed diffusion layer is also taken into account. The numerical solution of the consequent system of differential equations is achieved with the use of a non-linear shooting scheme in conjunction with the multidimensional Newton algorithm [1]. The space is discretized through a constant-step mesh while the resulting nonlinear system of ordinary differential equations is solved by using the 4th order Runge-Kutta method. The present numerical scheme for the determination of the spatial distributions of the concentration and the current density has been validated for the case of methanol according to the results in [2]. Various types of 2-D fuel cells configurations (namely: direct fuel, SOFC and PEM) are considered in this study while the feeding fuel is assumed to be either pure hydrogen or methane or methanol. The results are presented in terms of fuel crossover, which could be a serious problem for the effective operation of such power systems.