It is generally accepted to use the solar wind ram pressure ρV2 and the IMF Bz component for empirical description of the geo-magnetopause position and shape. A specific feature of the present paper is not to use the solar wind ρV2 but the thermal Pth and magnetic field Pmag pressures adjacent to the magnetopause for proper modelling. These pressures are deduced from the results of 3-D MHD runs and analytic solutions for post bow shock MHD flow in Lagrangian variables. The magnetopause shape variation due to Bz component changes the so called ‘doubling factor’ fd, which can be analytically deduced from a Tsyganenko magnetospheric field ellipsoidal model. Including all the above effects in our analytical model leads to a good description of ‘rapid’ magnetopause approach to the Earth for southward IMF and to its ‘stagnant’ behaviour with the increase of northward IMF component.