Abstract We report a testing of the earlier developed in the Institute of Mechanics of the Bulgarian Academy of Sciences numerical data-based 3D model of the system magnetosphere–magnetosheath with real satellite data. The model is a result of a self-consistent solution of two tasks: (i) Chapman–Ferraro problem for an arbitrary 3D magnetopause with an application of data-based internal magnetic field system, taken from the Tsyganenko magnetosphere models (T96 and T01); (ii) 3D numerical solution of the magnetosheath in a gasdynamic approach. Positions and shapes of the bow shock and the magnetopause are results of the solution and the appropriate application of the Rankine–Hugoniot conditions on both magnetosheath boundaries. Input parameters for the model are the solar wind plasma and magnetic field parameters, Dst index, and the Earth's dipole tilt. Ion flux measurements in the magnetosheath from the Interball-1 satellite were compared with model predictions. We used one magnetosheath crossing from the magnetopause (MP) to the bow shock (BS). For this case simultaneous WIND data served as a solar wind and interplanetary magnetic field monitor. Dst index was taken from the Kyoto database. An appropriate procedure was applied to normalize data values and spatial distances. A satisfactory coincidence with the observed plasma flux behavior along the trajectory, as well as the BS and MP positions are obtained in several cases. The discussed results seem to be rather optimistic about the model capabilities. It is worth noting that this idealized single-fluid model is not supposed to describe a large level of the plasma and magnetic field variations in the magnetosheath.