The problem of diffraction of a normally incident plane wave by a wedg
e with thin material coatings is studied. The thin coatings are simula
ted by the generalized impedance boundary conditions of the third orde
r. At the points of junction of the coatings, that is, on the edge of
the wedge, additional constraints are formulated. These constraints, o
r contact conditions, ensure uniqueness of the solution in the diffrac
tion problem. The solution is determined in an explicit form by means
of the Maliuzhinets' technique. The uniform and local asymptotics of t
he far field are deduced.