The properties of materials near structural phase transitions are often successfully described in the framework of Landau theory. While usually the focus is on phase transitions, which are induced by temperature changes approaching a critical temperature Tc, here we will discuss structural phase transformations driven by high hydrostatic pressure, as they are of major importance for understanding processes in the interior of our earth. Since at very high pressures the deformations of a material are generally very large, one needs to apply a fully nonlinear description taking physical as well as geometrical nonlinearities (finite strains) into account. In particular it is necessary to retune conventional Landau theory to describe such phase transitions. In [A. Tröster, W. Schranz and R. Miletich, Phys. Rev. Lett.88, 55503 (2002)] we have constructed a Landau-type free energy based on an order parameter part, an order parameter-(finite)strain coupling and a nonlinear elastic term. This model provides an excellent and efficient framework for the systematic study of phase transformations for a wide range of materials up to ultrahigh pressures. We illustrate the model on the specific example of BaCr(Si 4 O 10 ), showing that it fully accounts for the elastic softening which is observed near the pressure induced phase transformation.