The diffraction by a wedge coated with multi-layer dielectric laminate is a problem of interest in many different applications. In spite of many efforts which can be traced back to the late 1950s a general solution to the problem is not yet available. By using first and second order impedance boundary conditions on the wedge faces, some useful techniques have been developed. However further generalization has not yet been carried out because of the difficulties of applying these techniques to higher order boundary conditions. We use the most general (the infinite order) generalized impedance boundary condition (GIBC) model for the analysis of diffraction by an impedance wedge with multi-layer coatings on its faces. A summary of formulation and solution of the problem are described for the 2D case (the normal incidence). Generalization to the 3D case is possible for the special values of exterior wedge half angles /spl phi/=/spl pi/ and /spl pi//2, using an approach similar to what has been suggested for simple impedance wedges.