A body force distribution method is presented for the torsion problem of a rigid circular cylinder embedded in an infinite elastic thick plate. Here we apply a new Green's function for torsion problems of an infinite elastic thick plate in order to consider the stress singularity. The stress distributions of the problem were investigated in a previous paper. This paper deals with the order of stress singularity at the bottom corner of the cylinder. Luco investigated the torsion problem of a rigid cylinder embedded in an elastic half space and showed λ=1/3 for the order of singularity.