Continuing their earlier work on strain energy functions of homogeneous isotropic compressible materials that admit special isochoric deformations, i.e. torsion and axial shear of a tube, the authors study the possibility of circumferential shear of an infinitely long tube bonded to a rigid core. They derive conditions for the strain energy function and discuss certain classes, which comply with them, in detail. These contain as special cases strain energy functions well known in finite elasticity. The authors show that a tube whose surface is free of radial stress, in addition to zero radial displacement, cannot undergo isochoric circumferential shear. This well written paper is of interest to researchers in finite elasticity.