In this paper, formulation of the problem of plane wave diffraction by a wedge with anisotropic impedances is given for the case of almost grazing incidence. All steps of problem are given in detailed. Wedge is a canonic structure and diffraction from wedge may be used in modelling scattering from a variety of complex structures. In this study, by using the Maxwell’s equations the field components can be expressed in terms of z-components. By applying appropriate boundary conditions, a coupled system of equations is obtained in terms of field component and derivatives of field components with respect to  and r. By using similarity transform to the coupled system of equations, the coupling is reduced to the simplest form in which Malyuzhinets theorem can be applied. The solution of field components is sought in the form of Sommerfeld integrals. The Malyuzhinets theorem is applied to the Sommerfeld integrals. By using Sommerfeld integrals the problem is reduced to a system of coupled functional equations. Solution of homogeneous functional equations is given in terms of χф functions. For a small parameter of the problem (sinθ0<<1 where θ0 is the angle between z-axis and incident wave) the perturbation procedure is used to reduce the coupled functional equations to a system of linear equations with this small parameter being at the integral terms of equations. As a result the closed form solution is given for functional equations. The obtained analytic expression for the spectral functions is substituted to the Sommerfeld integrals, which are evaluated by means of steepest descent technique.Then, the analytical expressions for the diffraction coefficient for both magnetic and electric field components are derived. Considering these different geometries and small skewness angle, it is concluded that this approach enlarge the class of solvable diffraction problem in a small range. Additionally, the results are valuable for the comparison purposes for the other approximate methods. Manuscript profile