Equivalent Medium theory tries to predict the gross behavior of a heterogeneous medium. While there exist theories for calculating equivalent homogeneous counterparts for special geometries, most of them consider isotropic solids or isotropic solid-fluid media. Recently Schoenberg and Muir (1989) introduced an elegant averaging scheme for anisotropic horizontal layers. That scheme demands layers with thicknesses much smaller than the length of the elastic wave which is propagating through it. It is a static approach, but results show that in the long-wavelength limit reasonable results can still be obtained. A more general averaging scheme would have two objectives: allow arbitrary geometry and lift the static assumption. In this paper I show a way to describe a heterogeneous anisotropic medium and relate it to an equivalent homogeneous counterpart by requiring integral equivalence. The way of defining equivalence is of uttermost importance. In the following I assume equivalence as outlined for the Schoenberg & Muir scheme by Nichols and Karrenbach (1990). Generalizing that notion, a heterogeneous medium and its homogeneous counterpart exhibit the same mass, the same changes in volume and the same deformation energy. If a stress is applied to the exterior surface of a heterogeneous body, the homogeneous equivalent shows identical change in deformation energy within and the same average displacements and forces on its boundaries.