Our model of a direct methanol fuel cell with straight channels is extended to take into account finite conductivity of current collector plates and local contact resistances. Co-flow conditions are assumed and the two cases are considered: (i) when load resistor is connected at the inlet of the feed channels and (ii) when it is connected at the outlet. In both cases voltage loss in the plates induces growth of current production close to the point of load connection. The increase in local current j is accompanied by the growth of local polarization voltages η a and η c of the anode and the cathode sides, respectively. Moving the point of load connection one can change the distribution of j , η a and η c along the channel. Local “spot” of contact resistance decreases local current and polarization voltages; in the rest part of the cell these values increase.