This paper presents theoretical aspects of wave propagation in a transversely isotropic medium, aimed at providing a framework within which cross-hole (CH), down-hole (DH) and seismic dilatometer tests (SDMT) can be correctly interpreted. In particular, as an example, tests performed at the well documented Fucino site, with the source located at various distances from the sounding, indicate the capability of SDMT to detect the ratio Ghh /Gvh.