This paper gives the solution to the torsion problem for a near‐cylindrical shaft of circular section having a toroidal cavity. Since the interpretation of the axially symmetric problem as a flow problem in 5 dimensions is well known, the first part of the paper is devoted to developing a method for handling the flow problem about anndimensional ring‐shaped body of general cross section. In the second part of the paper this method is applied to the case of anndimensional torus ring. The casen=3 then yields the solution to the classical flow problem, andn=5 gives the solution to the torsion problem under consideration.