Abstract <p>Solutions to a problem of a solid circular rod made of orthotropic creep material and subjected to torsion by a constant torque are generalized to the case of an annular rod. Calculations are carried out using the Bhatnagar–Gupta method, the method based on the principle of minimum additional dissipation, and the finite element method. It is shown that the characteristic parameter method can be used to estimate a stress-strain state. The resulting analytical dependences of the twist angle rate on time at the steady-state stage of creep can be used to determine the shear parameters of the orthotropic Hill potential in torsion experiments or to refine them if these parameters were obtained via other approaches.</p>