We extend the Neuber-Papkovich potentials to the computation of particular solutions for the Cauchy-Navier equations of elastodynamics with nonhomogeneous forces. For a related boundary value problem, we use the developed representation to approximate a particular solution by superposition of plane wave functions with different frequencies and directions of propagation. The homogeneous part of the solution is then approximated via the method of fundamental solutions. Numerical experiments are presented in order to discuss the feasibility and accuracy of the proposed method.