The authors study the unconstrained (free) motion of an elastic solid \(\mathcal B\) in a Navier-Stokes liquid \(\mathcal L\) occupying the whole space outside \(\mathcal B\), under the assumption that a constant body force \(\mathfrak b\) is acting on \(\mathcal B\). More specifically, the authors are interested in the steady motion of the coupled system \(\{\mathcal B,\mathcal L\}\), which means that there exists a frame with respect to which the relevant governing equations possess a time-independent solution. The authors prove the existence of such a frame, provided some smallness restrictions are imposed on the physical parameters, and the reference configuration of \(\mathcal B\) satisfies suitable geometric properties.