The stationary 3D MHD model of a quiescent solar prominence is presented. The components of the magnetic field depend on three variables (x, y, z) in the Cartesian coordinate system, the filament is located above the photospheric line of polarity inversion. The prominence has maximum thickness in the middle part where the plasma flow (Alfven Mach number) reaches the maximum value too, and it becomes thinner at the ends where plasma flow disappears. The choice of the ratio of the prominence length to its cross section is arbitrary: both short and very long filaments can be modeled. The thermodynamic parameters of steady state of the system (gas pressure, density and temperature) are calculated in accordance with a prescribed structure of the magnetic field. The external environment is determined by the hydrostatic model of the solar atmosphere. The prominences plasma parameters obtained in the model are in good agreement with the observational data.