A one-dimensional two-phase model has been developed for a direct methanol fuel cell (DMFC) and flowing electrolyte - direct methanol fuel cell (FE-DMFC). The model has been compared to experimental data found in literature and corresponds well. Using this model, the performance of the DMFC and FE-DMFC are evaluated and compared to one another as well as to their respective single phase models. It has been found that there is a substantial difference between a two-phase and single phase model. Furthermore, the FE-DMFC outperformed the DMFC when it came to methanol inlet concentrations and varying operating temperatures due to the FE-DMFC's ability to reduce the methanol crossover.