Consider the scattering of an electromagnetic time-harmonic plane wave by an infinite cylinder having STRESS-FX STRESS FORMULA an open crack and a bounded domain in as cross section.We assume that the crack is divided into two parts, and one of the two parts is (possibly) coated on one side by a material with surface impedance.Different boundary conditions are given on and.Applying potential theory, the problem can be reformulated as a boundary integral Sofas system.We obtain the existence and uniqueness of a solution to the system by using Fredholm theory.