This paper presents some fundamental concepts of seismic anisotropy specifically those which have hexagonal symmetry (ordinarily called transversely isotropic in geophysics jargon). There were made calculations of phase and group angles at a planar interface separating an anisotropic media, using routines written in Matlab ® and Maple ® language. The slowness surfaces of the qP, qSV and SH wave, as well as the ray paths in these two media were also estimated. Although only the simplest situations are discussed, this paper is useful as a first step in understanding the fractured media, because it contains examples, software routines, and a reviewing of the basic concepts and formulas of wave propagation.