This paper describes a multi-step strong coupling method to analyze an equation system of incompressible viscous fluid and an elastic body. The procedure is derived based on the following techniques; (a) sub-structuring, (b) velocity-pressure splitting, and (c) time integration of Newmark's family. Only simultaneous equations with well-defined symmetric matrices are solved in the method. To demonstrate fundamental performance of the method, it is applied to solve an impacted beam in fluid. The result shows good agreement with a previous work.