In this paper an approximate analytical solution for constrained high-pressure torsion problem is proposed. The finite-strain elastic–plastic model based on multiplicative split of deformation gradient tensor is utilized. Plastic deformation is described by non-associative flow rule. Thus, the dependence of the plastic properties of the material on pressure is taken into account. The problem is reduced to a boundary value problem with a moving boundary for a coupled nonlinear hyperbolic system. The obtained approximate solution is constructed under the assumption of a stationary pressure field in the plastic region, which agrees with the experimental results and also with the exact solution for pressure insensitive material; this analytical solution is very close to the numerical one. The closed-form expressions are obtained for stress tensor and accumulated plastic strain. The effects of the material properties, as well as the value of the initial pressure on the distribution of local mean stress and on the accumulated plastic strain are investigated. Simple analytical condition for cohesion-to-slip transition on the contact surfaces between sample and anvils is obtained. At the same time, this transition sets a limit on the applicability of the obtained solution. With the pressure sensitivity coefficient tends to zero, the approximate solution tends to an exact analytical elastic–plastic solution in the framework of the associative plasticity. Stress inhomogeneity in the presented solution is a consequence of nonlinear elastic effects in the main. For hard materials with small elastic deformations the presented solution predicts almost uniform stress distribution. At the same time, stress inhomogeneity in HPT of hard materials can be significant, and is a consequence of inhomogeneity of the initial pressure, strain inhomogeneity due to deformation of the gasket, as well as phase transformations of the material. For this reason the presented solution utility is restricted to soft hyperelastic materials.