The interaction problem of an elastic structure and an incompressible viscous fluid issolved through a computational procedure proposed in this paper.The fluid region is considered to bebounded though without free surface boundary.The discrete fluid domain is described by the stream-line upwind/Petrov-Galerkin finite element method.The arbitrary Lagrangian-Eulerian description isemployed to treat the moving interface between the structure and the fluid.The predictor-multicorrec-tor method is adopted to solve the coupling finite element equations.The results of three numerical ex-amples show the effectiveness of the procedure.