A mathematical model for the simulation of the transport phenomena occurred in the anode of a typical fuel cell is presented here. The model initially considers a simple one dimensional geometry where the mass transport equation is combined with a Tafel-type description for the current density. By assuming isothermal conditions, the numerical solution of the differential equations was achieved with the use of a non-linear shooting scheme in conjunction with the multidimensional Newton algorithm. The space was discretized through a constant-step mesh while the resulting nonlinear system of ordinary differential equations was solved by using the 4th order Runge-Kutta method. The whole algorithm was implemented by developing a new FORTRAN code. In addition, a planar two-dimensional geometry is also considered, where the mass transport is described by the convection-diffusion equation within the catalyst layer together with the Navier- Stokes equation for laminar flow conditions and the electrochemical effects, while the convective heat transfer within the developed diffusion layer is also taken into account. This approach has been numerically implemented and solved by using the finite volume method being applicable through the CFD-RC© commercial package. For the sake of simplicity, the feedstream of the fuel cell was assumed to be a hydrogen-rich mixture (H2 >90%) for all cases. Both SOFC and PEM type fuel cells were considered in this study, while the results are presented in terms of fuel concentration, produced current density and overpotential.