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The simulation of the results of metal testing under creep conditions at the nonstationary complex stress state is considered. As an example, we consider the experimental data obtained by a group of Japanese scientists for testing tubular samples of stainless steel under the temperature of $650 ^{\circ}$C. The following article presents the test results for four different loading programs. These loading programs are various combinations of piecewise constant dependencies of tangential and normal stresses on time. The presented data was simulated using the hardening theory and the flow theory; two material constants used are determined from the condition of the minimum relative integral discrepancy between the experimental and theoretical values of the corresponding creep deformations. A comparison was made of the results of the simulation carried out with the results of the simulation of the same experimental data, carried out by other researchers using other theories. In these theories, a large number of material characteristics are used: from three to nine constants and additionally one material function. The advantage of the hardening theory and flow theory with only two material constants each compared to the other theories has been shown.