Thin stamped bipolar plates (BPPs) are viewed as promising alternatives to traditional graphite BPPs in proton exchange membrane fuel cells. Metallic BPPs provide good thermal/electrical conductivity and exhibit high mechanical strength, to support the loads within the stack. However, BPPs manufactured by stamping processes are prone to defects. In this study, the effect of the tool’s geometry on the thin sheet formability is investigated through finite element simulation. Despite the broad variety of flow field designs, most of BPPs comprise two representative zones. Hence, in order to reduce the computational cost, the finite element analysis is restricted to these two zones, where the deformation induced by the stamping tools is investigated. The channel/rib width, the punch/die fillet radii, and the channel depth are the parameters studied. The analysis is conducted for a stainless steel SS304 with a thickness of 0.15 mm. The results show that the maximum value of thinning occurs always in the U-bend channel section, specifically in the fillet radius of the die closest to the axis of revolution.