Abstract: We first derive the system of incompressible isotropic elastodynamics in Eulerian coordinates incorporating divergence-form nonlinear terms and external forces in three dimensions. Then by employing the invariance of the corresponding stationary system under translation, spatial rotations and scaling, we use the generalized energy estimates and the standard contraction mapping theorem to obtain the existence and uniqueness of the stationary solution for incompressible isotropic elastodynamics with external force, provided that the external force is time-indepedent and sufficiently small.