A numerical method is presented for calculating 3-D unsteady flow through bileaflet heart valves and flexible obstruction. The method combines finite volume, finite element, and overlapping grid methods. The employed overlapping grid method decomposed the entire domain into the solid region, the fluid region in the vicinity of the solid (the inner region), and the outer fluid region. A finite volume scheme was implemented for the outer fluid region, while a finite element scheme was employed in the solid and inner fluid regions. Calculations were carried out for the full 3-D valve geometry under steady inflow conditions with the Reynolds number ranging from 400 to 1200. The numerical results illustrate the evolution of the downstream vortices. The changes in the location and size of the reattachment vortices in response to the change of elastic modulus of solid and Reynolds number of fluids were recorded and tabulated. The results provide the detailed information sketching the evolution of the fluid-structure interaction in terms of the modes and amplitude.