In this paper, a method of superposition in given for the determination of approximate stress function of prisin with small hole in torsion. The approximate stress function consists of two parts. The first part is the solution of torsion problem for a simply connected region bounded by the exterior boundary of the given prism. The second part is the solution of Von-Neumann problem in the exterior region of the small hole.The boundary value of second part on the small hole is determined so that the superposition of these two solution gives free boundary condition on the surface of hole. It can be shown that the effect of second solution are concentrated in around the neighbourhood of the small hole.