A two-dimensional across-the-channel mathematical model for the simulation of a direct methanol fuel cell is described. The model accounts simultaneously for electrochemical kinetics, hydrodynamics, and multicomponent transport. The two-dimensional distributions of concentrations of reactants, the two-dimensional distributions of current densities, the crossover flux of methanol from the anode to the cathode, and current-voltage curve for the fuel cell have been calculated. The obtained results indicate that the concentrations of reactants in the catalyst layers in front of the current collectors are very low, which reduce the utility of catalyst; the current density at the edges of the channels is many times greater than the mean current density, which may lead to local overheat.