In the talk we address a system of PDEs describing an interaction between an incompressible fluid and an elastic body. The fluid motion is modeled by the Navier-Stokes equations while an elastic body evolves according to an linear elasticity equation. On the common boundary, the velocities and stresses are matched. We discuss available results on local well-posedness and prove new existence and uniqueness results with the velocity and the displacement belonging to low regularity spaces.