Abstract <p>The work is devoted to the theoretical study of the problem of identifying an inhomogeneous stress-strain state (SSS) in thick-walled tubular and solid samples loaded with axial force, torque, external (and for tubes – and internal) pressure. Unlike standard tests with thin-walled tubes, in this case it is possible to achieve significantly higher values of deformations before the loss of bearing capacity of the samples. A well-known approach to solving this problem is the conditional tube method, which requires two coordinated experiments on similar loading programs to identify the SSS. The paper provides a theoretical justification for the conditional tube (and degenerate conditional tube) method, taking into account the finite deformations in the sample.</p>