Consider the differential operator H= - μ(x)-1Δ in the Hubert space X = L2(RN; i(x)dx), where Δ is the Laplacian in RN, and μ(x) is a positive simple function on RN. Let S be the surface on which is discontinuous (the separating surface). So far the stratified media in which the separating surface S consists of parallel surfaces have been vigorously studied. Also the case where S has a cone shape has been discussed. In this work we shall deal with a new type of discontinuity which we call cylindrical discontinuity. Under this condition we shall use the limiting absorption method to prove that H is absolute continuous. Our method is based on a priori estimates of radiation condition term. © 1997, Walter de Gruyter. All rights reserved.