In this paper we consider an initial and boundary value problem that models the self-propelled motion of solids in a bidimensional viscous incompressible fluid. The self-propelling mechanism, consisting of appropriate deformations of the solids, is a simplified model of the propulsion mechanism of fish-like swimmers. The governing equations consist of the Navier-Stokes equations for the fluid, coupled to Newton's laws for the solids. Since we consider the case in which the fluid-solid system fills a bounded domain we have to tackle a free boundary value problem. The main theoretical result in the paper asserts the global existence and uniqueness (up to possible contacts) of strong solutions of this problem. The second novel result of this work is the provision of a numerical method for the fluid-solid system. This method provides a simulation of the simultaneous displacement of several swimmers and is tested on several examples.