In the frame of the DGMK-Project 741-2 we contribute to the understanding of the stress dependency of anisotropic seismic velocity as background for seismic forward modeling (e.g. constuction of macro model for imaging) and the interpretation of seismic data with respect to pore pressure, effective stress tensor and lithology. We use the physically based porosity deformation approach for description of compliances in dry or drained anisotropic rocks. We improved the predictability of velocities by e.g. accounting for stiff porosity next to compliant porosity. We include the description of non-diagonal elements using the assumption of anellipticity and of an isotropic piezosensitivity tensor. We performed and explained supporting experiments under uniaxial loading conditions using various types of room dry sedimentary rocks with VTI and originally HTI symmetry. Furthermore we investigated the impacts of pore fluids in a sandstone and a fine grained posidonian limestone. The main effects are the Gassmann effect and local fluid flow. We conclusively explained our measurements in the fully saturated sandstone by combining velocity predictions by means of the porosity deformation approach in drained rocks with classical poroelastic models. Additionally measurements in shales under hydrostatic and triaxial loading conditions have been performed in cooperation with an external company and subsequently evaluated.