In the presented work, we investigated the potential capabilities of contrast improvement in soft tissue achieved by x-ray phase contrast imaging. The Talbot-Lau interferometer method was implemented by means of x-ray diffraction gratings. Tomographic measurements were performed on prepared sam- ples containing specimens of different kinds of soft animal tissue. The results showed that phase contrast can provide additional and complementary visualization of soft tissue structures that are invisible to conventional, attenuation contrast x-ray imaging. As an example, the results obtained from the tomography of a bovine artery show that whereas the fat and connective tissue present around the artery can be seen with both absorption and phase contrast, the artery itself can only be recognized in the phase contrast image. Moreover, the situation is even more complicated for specimens containing not only soft tissue but also stronger absorbers such as bones or cartilage. Indeed, the strongly absorbing bones also lead to the scattering of the x- ray beam (due to their dense micro-structure), which results in a loss of the phase information. However, this issue relaxes when higher x-ray energies are used. Measurements of specimens (containing bones and soft tissue) were demonstrated with the set-up optimized for a mean x-ray energy of 50keV.