Abstract: In this paper. we use the complex function method for solving the problem ofinteraction of plane SH-waves and circular cavity surfaced with lining in anisotropicmedia.Anisotropic media can be used to simulate the conditions of the geology Thisproblem can be handled by using the method similar to that incorporated in Ref [5] todefine the scattering waves in media. added with the given boundary condition of the circular cavity. In this paper. as illustrated in the examples the results and discussions ofnumerical studies have been done for the interaction of plane SH-waves and two kinds of circular cavities surfaced with lining made up of different materials in anisotropicmedia.