By analyzing the problem of high pressure torsion (HPT) in the rigid plastic formulation, we show that the power hardening law of plastically deformed materials leads to self-similarity of HPT, admitting a simple mathematical description of the process. The analysis shows that the main parameters of HPT are proportional to βq, with β being the angle of the anvil rotation. The meaning of the parameter q is: q = 0 for velocity and strain rate, q = 1 for shear strain and von Mises strain, q = n for stress, pressure and torque (n is the exponent of a power hardening law). We conclude that if the hardening law is a power law in a rotation interval β, self-similar regimes can emerge in HPT if the friction with the lateral wall of the die is not too high. In these intervals a simple mathematical description can be applied based on self-similarity. Outside these ranges, the plasticity problem still has to be solved for each value of β. The results obtained have important practical implications for the proper design and analysis of HPT experiments.