An elastic and compressible material occupies a bounded domain Omega subset of R-n, n greater than or equal to 2, for any time t is an element of [0, T], T > 0 being given. This material is subject to a body force F : [0, T] x Omega --> R-n of the form F(t, x) : = rho(t)f(x), where f : Omega --> R-n is supposed to be unknown. The evolution of the displacement vector field is described by a Cauchy-Dirichlet problem for the linear elastodynamics system. We study the inverse problem of identifying f by measuring the traction g exerted on a portion Gamma of the boundary partial derivative Omega over the time interval [0, T]. Using exact controllability methods, we show uniqueness and continuous dependence results. Also, we prove a representation formula for f in terms of g.