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.