The wall shear stress induced by the leaflet motion during the valve-closing phase has been implicated with thrombus initiation with prosthetic valves. Detailed flow dynamic analysis in the vicinity of the leaflets and the housing during the valve-closure phase is of interest in understanding this relationship. A three-dimensional unsteady flow analysis past bileaflet valve prosthesis in the mitral position is presented incorporating a fluid-structure interaction algorithm for leaflet motion during the valve-closing phase. Arbitrary Lagrangian-Eulerian method is employed for incorporating the leaflet motion. The forces exerted by the fluid on the leaflets are computed and applied to the leaflet equation of motion to predict the leaflet position. Relatively large velocities are computed in the valve clearance region between the valve housing and the leaflet edge with the resulting relatively large wall shear stresses at the leaflet edge during the impact-rebound duration. Negative pressure transients are computed on the surface of the leaflets on the atrial side of the valve, with larger magnitudes at the leaflet edge during the closing and rebound as well. Vortical flow development is observed on the inflow (atrial) side during the valve impact-rebound phase in a location central to the leaflet and away from the clearance region where cavitation bubbles have been visualized in previously reported experimental studies.