Three-dimensional electromagnetic scattering of plane waves from a class of anisotropic impedance wedges is analyzed. All the configurations considered are characterized by anisotropic impedance faces with their principal anisotropy axes parallel and perpendicular to the edge, with one of the two elements characterizing the impedance tensors vanishing or diverging. Rigorous integral representations for the field are determined by resorting to the Maliuzhinets’ method; they are defined along the Sommerfeld's integration path, so that are suitable for their asymptotic evaluation. Although valid only for specific configurations, we note that the new rigorous solutions can be used for testing the accuracy of numerical or approximate analytical methods, applicable to more general cases. The particular category of impedance tensors considered for the wedge faces can be usefully applied for analyzing the specific case of the artificially hard and soft surfaces.