Abstract <p>Combined torsional and circular shear of an incompressible nonlinear-elastic right-circular hollow cylinder is studied. A solution of the problem is obtained for an arbitrary elastic potential depending on the first invariant of the left Cauchy – Green deformation tensor solely (generalized neo-Hookean solid). For the Gent material, closed-form analytical solution is obtained. A rotary damper design based on the obtained solution is proposed. Formulas for the dissipation of kinetic energy caused by friction on the cylindrical surfaces of the pipe are derived. For a strain softening material, a numerical solution, which is compared with experimental results, is obtained.</p>