The theory of elastic plane wave propagation has been applied to the specific case of a convergent acoustic beam inside an anisotropic material. The result of this theoretical analysis is used to determine the general expression for a convergent beam propagating in an anisotropic specimen. By using an asymptotic expansion around points of stationary phase, one can write a simple analytic approximation that has much in common with the geometric ray theory, while also containing useful amplitude information. The approximate result is not restricted to any specific problem since it was derived without concern for boundary conditions. The result is efficiency in computation that would be missing from a fully accurate wave theory. These theoretical results also confirm some previous theoretical and experimental analyses^9,16–17 concerning quasi-2D crystals (graphite and HTS materials), and which also may be applied to ferroelastics near the ferroelastic transition, ordered composites, matrix metals, and other materials. Acoustomicroscopical visualisation was achieved using the more favourable features of the propagation of convergent acoustic beams in anisotropic media. The lateral resolution of an acoustic microscope in that case can be reached up to the order of a wavelength in the liquid couplant for any depth inside the material. Because we can achieve high contrast at significant depths, it is possible to use these results as a useful and powerful method to study the bulk structure of materials.