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era dif utio s e und he eri ew ts isl nho te ty 33 method is based on the assumption that elastic mismatch between dissimilar materials is negligible. Recently, the Faber series method 11 has been employed to study the problem of an arbi-1 2 domain S2 and assume that the inhomogeneity occupies the region S1. The interface L separating the inhomogeneity and the sur-Downloatrary shaped inclusion perfectly bonded to the surrounding matrix. In particular, Gao and Noda 12 use the Faber series method to investigate the anti-plane problem of an arbitrary shaped piezo-electric inclusion embedded in an infinite piezoelectric medium. The focus of the current paper is to investigate, in detail, the interaction problem of a screw dislocation with an arbitrary shaped elastic inhomogeneity. The main feature of this work is that the material properties of the inclusion and the surrounding matrix are different. The solution, in series form, is obtained by means of complex variable methods and Faber series expansion. A rigid inclusion or a cavity can be treated as a special case by letting the shear modulus of the inhomogeneity become infinite or zero, respectively. Once the solution is obtained, the stress fields in the inhomogeneity and in the matrix can be derived. In addi-rounding matrix is assumed to be perfect i.e., both the displace-ment and traction vectors are continuous across L. In addition, a screw dislocation with Burgers vector b is located at the point z =z0 in the matrix. For the anti-plane problem discussed in this paper, the displace-ment u3, the stresses 31,32, and resultant the force R3 along any arc can be expressed in terms of a single analytic function fz as u3 = Imfz , 32 + i31 = fz , 1 R3 = − Refz . We consider the following conformal mapping function z = m = R + n=1 m