This paper introduces a structured procedure to optimize the internal structure (relative sizes, spacing) and external shape (aspect ratios) of a single alkaline membrane fuel cell so that net power is maximized. The optimization of flow geometry is conducted for the smallest (elemental) level of a fuel cell stack, i.e., the single alkaline membrane fuel cell, which is modeled as a unidirectional flow system. The polarization curve, total and net power, and efficiency are obtained as functions of temperature, pressure, electrolyte solution concentration (KOH), geometry and operating parameters. The optimization is subjected to fixed total volume. There are two levels of optimization: (i) the internal structure, which basically accounts for the relative thicknesses of two reaction and diffusion layers and the membrane space, and (ii) the external shape, which accounts for the external aspect ratios of a square section plate that contains all single alkaline membrane fuel cell components. The available volume is distributed optimally through the system so that the net power is maximized. Temperature and pressure gradients play important roles, especially as the fuel and oxidant flow paths increase. The optimized internal structure and external shape are a result of an optimal balance between electrical power output and pumping power required to supply fuel and oxidant to the fuel cell through the gas channels. In the process, a third level of optimization was found with respect to the KOH concentration in the electrolyte solution that leads to a 3-way maximized net power output. The numerical results show that the maxima found are sharp, since a variation of up to 600% in net power was observed within the tested range of AMFC external aspect ratios, what emphasizes the importance of finding the optimal AMFC parameters, no matter how complex the actual design might be. It is also shown that the three times maximized net power increases monotonically with total volume raised to the power 0.7 (~3/4), similarly to metabolic rate and mass in animal design. Due to the fact that precision and low computational time are combined, it is expected that the model could be used as an important tool for AMFC design, control and optimization at the fuel cell stack level.