In this paper we examine the classical problem of finite bending of a rectangular block of elastic material into a sector of a circular cylindrical tube in respect of compressible transversely isotropic elastic materials. More specifically, we consider the possible existence of isochoric solutions. In contrast to the corresponding problem for isotropic materials, for which such solutions do not exist for a compressible material, we determine conditions on the form of the strain-energy function for which isochoric solutions are possible. The results are illustrated for particular classes of energy function
