To see the similarities and differences with eletromagnetics, basic concepts and equations of elastodynamics are formulated in coordinate-free form applying concepts from Polyadic Algebra. Plane-wave propagation is studied for time-harmonic equations in isotropic and simple uniaxially anisotropic media and the Green dyadic is derived for the isotropic medium. As an extension, the Green dyadic for the anisotropic elastic medium is derived in perturbational approximation. In the Appendix A, some basic properties for tetradics, useful for practical analysis both in elastodynamics as well as in electromagnetics, are derived.