Karal and Keller [1] developed the geometrical acoustics for wave propagation in a heterogeneous isotropic medium, generally adopting the methods used in geometrical optics [2,3]. It is very difficult to find a solution for wave propagation in a heterogeneous anisotropic medium. Here, instead of finding an exact solution, we extend the geometrical acoustics to a heterogeneous anisotropic medium to untangle the behavior of wave fronts spreading into an undisturbed region. The eikonal equation which contains information of the phase and group velocities, along with the transport equation which governs the amplitude of propagating waves, are derived. For a one-dimensionally heterogeneous anisotropic solid, wave propagation is two dimensional and it is possible to obtain closed-form analytic formulas for the ray path and travel time of a ray. These formulas are applied to find the path and travel time of rays generated from a pointlike source and detected by a small detector. The predicted arrival times agree well with observed values.