The computational fluid dynamics (CFD) study of the mass and heat transfer in the phosphotungstic acid electrolyte-based fuel cell (PWAFC) was performed in order to elucidate the cause of irregular fuel cell work failures at high current densities, which manifested through partial melting of the matrix and electrodes and crossover effect. It was established that the reason for these difficulties is not the damage (cracks) of the catalyst layer in the gas diffusion electrode, but the bad construction of the reactant gas and liquid electrolyte distributors on cathode and anode side of the PWAFC and the lack of cooling system. The CFD study pointed to several practical conclusions how to improve the PWAFC construction.