This research work is given up to mathematical and numerical modeling of the medium flow on the centrifugal pump stage often used to produce hydrocarbons on oil fields. Defined problem is very complicate problem in physics and mathematics due to 3D channel features including flow rotations by wide angles and rotating elements. The considered flow is viscous and turbulence and requests usage of high level mathematical models. The initial-boundary problem for partial differential equations describing 3D non-steady viscous turbulence fluid flow on the pump stage (Reynolds averaged Navier–Stokes equations) is formulated in this work. The turbulence model is $k$-$\varepsilon$. The numerical method is finite-difference scheme with second order of accuracy. The 3D model of the pump stage was build using 3D automated layout system and it was created the computational grid after that (1600000 cells). The multiple runs were conducted using Fluent 6.2 Solver. The results allowed to obtain detailed distribution of the flow parameters within stage and to estimate possible critical situations in the pump performance. Note that there are currently no experiments giving the distribution of the flow parameters within pump stage. The results of the numerical modeling were analyzed, the integral parameters were obtained and compared with experimental data and simple analytic model [1]. Simple model has significant difference with both the computational results presented in this work and the experimental data.