The diffraction of plane waves obliquely incident on the edge of anisotropic impedance half and full planes is investigated. Homogeneous anisotropic impedance boundary conditions are defined on both faces of the canonical structures under study, the principal anisotropy axes being parallel and perpendicular to the edge. Rigorous integral representations for the longitudinal field components are derived by applying the Sommerfeld-Maliuzhinets method for a set of specific electrical configurations. Explicit uniform asymptotic expressions for the fields are given in the format of the Uniform Geometrical Theory of Diffraction (UTD). Although obtained for a specific class of geometrical and electrical configurations, these high-frequency solutions provide a contribution for investigating the effects of material anisotropy on edge diffraction, as they represent a new set of reference cases for either developing perturbative solutions or testing numerical and approximate analytical methods of more general validity. Furthermore, these solutions extend the applicability of the Sommerfeld-Maliuzhinets technique and represent a step forward to the solution of more general wedge canonical problems.