In this paper we consider the problem of single circular elastic inhomogeneity embedded within a circular cylinder whose curved boundary surface is subjected to surface traction acting on axial direction. We investigate the displacement neutrality of the coupled system of host body and inclusion. Neutral inhomogeneity (inclusion) does not disturb the displacement, strain and stress fields in the host body. The deformation of the considered inhomogenneous cylinder is antiplane shear deformation.