In order to clarify anisotropy effects on body wave propagation, exact transient solutions radiated from horizontal line sources of stress discontinuities in a transversely isotropic medium with a vertical axis of symmetry are formulated by a modified Cagniard method which gives the inverse Laplace transform in an ingenious manner. The advantage of the exact transient solutions is the clear onset of elastic displacements at the time of body wave arrivals that are defined by corresponding group velocities. The exact transient solutions display three principal effects of anisotropy: (1) noncircular propagation of wave fronts; (2) deviation of polarizations of particle motions of qP, qSV, and qSH waves from those in an isotropic medium; and (3) separation of group velocity from phase velocity, depending on the relative orientation of anisotropy and wave propagation directions. ¿American Geophysical Union 1990