Failure of synthetic heart valves is usually caused by tearing and calcification of the leaflets. Leaflet fiber-reinforcement increasesthe durability of these values by unloading the delicate parts of the leaflets, maintaining their physiological functioning. Theinteraction of the valve with the surrounding fluid is essential when analyzing its functioning. However, the large differences inmaterial properties of fluid and structure and the finite motion of the leaflets complicate blood-valve interaction modeling. This has,so far, obstructed numerical analyses of valves operating under physiological conditions. A two-dimensional fluid-structureinteraction model is presented, which allows the Reynolds number to be within the physiological range, using a fictitious domainmethod based on Lagrange multipliers to couple the two phases. The extension to the three-dimensional case is straightforward. Themodel has been validated experimentally using laser Doppler anemometry for measuring the fluid flow and digitized high-speed videorecordings to visualize the leaflet motion in corresponding geometries. Results show that both the fluid and leaflet behaviour are wellpredicted for di!erent leaflet thicknesses.