We conducted a series of calculations with the models of turbulent viscosity k–e, SST and three variants of three-dimensional unstructured computational grids. For each variant of the computational grid we calculated each of the two models of turbulent viscosity at axial velocity at input from 110 to 150 m/s. Comparison of results of numerical experiments with data of the physical experimental studies revealed that an error of the computational research is 0.3...8.6 %. Results of the study showed that at the first phase of calculation of the stage of an axial compressor one can recommend using the model of turbulent viscosity k–e and the coarse computational grid. To solve the problems on internal aerodynamics of compressors taking into account the flow in the near-border layer and aerodynamic trail, it is expedient to employ the model of turbulent viscosity SST and the fine adaptive grid.