We solve an axisymmetric problem of the interaction of harmonic waves with a thin elastic circular inclusion located in an elastic isotropic body (matrix). On both sides of the inclusion, between it and the body (matrix), conditions of smooth contact are realized. The method of solution is based on the representation of displacements in the matrix in terms of discontinuous solutions of Lame equations for harmonic vibrations. This enables us to reduce the problem to Fredholm integral equations of the second kind for functions related to jumps of normal stress and radial displacement on the inclusion.
Key words: harmonic wave of thin elastic circular inclusion,Bursting decision Lame equations, fluctuations Fredholm second kind.