Fluid-structure interaction computations in geometries where different chambers are almost completely separated from each other by a movable rigid body but connected through very small gaps can encounter stability problems when a standard explicit coupling procedure is used for the coupling of the fluid flow and the movement of the rigid body. An example of such kind of flows is the opening and closing of valves, when the valve motion is driven by the flow. A stability analysis is performed for the coupling procedure of the movement of a cylinder in a cylindrical tube, filled with fluid, Between the moving cylinder and the tube, a small gap is present, so that two chambers are formed. It is shown that a standard explicit coupling procedure or an implicit coupling procedure with explicit coupling in the subiterations steps can lead to unstable motion depending on the size of the gaps, the density of the rigid body, and the density of the fluid. It is proven that a reduction of the time-step size cannot stabilize the coupling procedure. An implicit coupling procedure with implicit coupling in the subiterations has to be used. An illustration is given on how such a coupling procedure can be implemented in a commercial computational fluid dynamics (CFD) software package. The CFD package FLUENT (Fluent, Inc.) is used. As an application, the opening and the closing of a prosthetic aortic valve is computed.