Membranes are a key component of proton exchange membrane water electrolysis (PEMWE) cells and are exposed to various stressors during operation, which can significantly reduce cell lifetime. PEMWE membranes incorporating woven web layers within the membrane structure for mechanical reinforcement are a promising, commonly used industrial strategy to mitigate the formation of membrane defects. Within this study the structural mechanics of a PEMWE cell is investigated, specifically the woven web reinforced membrane. Experimental tensile tests are conducted on the membrane to obtain stress-strain data. These measurements were utilized to parameterize a geometrically simplified model of the woven web reinforced membrane through a tensile test simulation. The validated model is applied in a 2D-cell simulation to identify resulting stresses and strains in the membrane during various electrolysis operation modes. The results herein allow the used PEMWE cell geometry to be systematically evaluated and optimized with respect to mechanical membrane stability. For the applied PEMWE cell setup, no failure is to expect during normal operation, including varied temperatures and differential pressure. Increasing the gap size at the edge of the electrochemically active cell area, however, leads to large deformations when the gap becomes larger than 0.2 mm.