The form of the Gaussian beam in an anisotropic medium has been found by solution of Maxwell's equations. For mathematical convenience a cylindrical beam (two-dimensional) is considered, with the field constant in one cross-sectional dimension and varying as the Gaussian function in the other. For uniaxial crystals, and for biaxial crystals where the propagation is in one of the principal planes, two solutions are obtained, corresponding to the ordinary and extraordinary waves. The Gaussian beam for the ordinary wave is identical to that for an isotropic medium. The extraordinary Gaussian beam is modified by double refraction and by an increase in the beam spread of ₁₁/₃₃. The properties of the extraordinary Gaussian beam are derived and applied to the problem of an optical resonator filled with an anisotropic medium. The low- and high-loss regions are found for the resonator together with its resonant frequencies. Two kinds of anisotropic cavity are distinguished: those where the optic axis of the medium is at 0° or 90° to the optical axis of the cavity and those where the optic axis is at 45° to the cavity axis. The three-dimensional Gaussian beam is treated by assuming that it can be represented by two orthogonal two-dimensional beams. The effect of anisotropy on the extraordinary beam gives rise to nonspherical wavefronts and elliptical cross sections. Some applications of the theory to laser problems are outlined.