The necessity of nondestructively inspecting cast steels, weldments, composites, and other inherently anisotropic materials has stimulated considerable interest in wave propagation in anisotropic media. Here, the problem of an ultrasonic beam traveling in an anisotropic medium is formulated in terms of an angular spectrum of plane waves. Through the use of small angle approximations, the integral representation is reduced to a summation of Gauss–Hermite eigensolutions. The anisotropic effects of beam skew and excess beam divergence enter into the solution through parameters that are simply interpreted in terms of the slowness surface. Both time harmonic and pulsed solutions are discussed. Formulas are also presented for transmission of a beam through a curved interface between two media. Examples are given illustrating how this method may be applied to predicting beam patterns during ultrasonic inspections.