AbstractNumerical simulations of cardiac blood pump systems are integral to the optimization of device design, hydraulic performance and hemocompatibility. In wave membrane blood pumps, blood propulsion arises from the wave propagation along an oscillating immersed membrane, which generates small pockets of fluid that are pushed towards the outlet against an adverse pressure gradient. We studied the Fluid–Structure Interaction between the oscillating membrane and the blood flow via three‐dimensional simulations using the Extended Finite Element Method (XFEM), an unfitted numerical technique that avoids remeshing by using a fluid fixed mesh. Our three‐dimensional numerical simulations in a realistic pump geometry highlighted, for the first time in this field of application, that XFEM is a reliable strategy to handle complex industrial problems. Moreover, they showed the role of the membrane deformation in promoting a blood flow towards the outlet despite an adverse pressure gradient. We also simulated the pump system at different pressure conditions and we validated the numerical results against in‐vitro experimental data.