The project aimed to describe the dependency of seismic velocity in anisotropic siliclastic rocks as background for interpretation of seismic data with respect to effective stress and lithology. We use the tensorial porosity-deformation approach for anisotropic rocks (originally piezo-sensitivity theory, Shapiro 2003; Shapiro and Kaselow 2005) and give an adapted formulation for vertical and horizontal transverse isotropic rocks under uniaxial and triaxial loading conditions. By using the porosity-deformation approach the number of free parameters is reduced compared to phenomenological fitting of data. With this theory we explain literature data of compliances measured in a shale sample during a multistage pseudo triaxial experiment. The obtained model parameters from fitting the hydrostatic part are used for the prediction of the compliances describing the S-waves in the triaxial part of data. Furthermore, we developed further an experimental setup and are now able to measure complete sets of velocity for the description of transverse isotropic and orthorhombic rocks. The new data reveal new aspects of the stress dependency of anisotropy parameter. The applicability of the theory on the new data and on previously obtained incomplete datasets is shown, including the reconstruction of velocities.