In a companion statistical study, we showed that the expression of the magnetopause surface as a power law of an elliptic function of the zenith angle θ holds at lunar distances, that the flaring of the magnetopause surface is influenced by the Interplanetary Magnetic Field (IMF) By component and that the IMF Bx component had no influence on the stand-off distance. As a follow-up to these statistical results, this paper presents a new empirical analytical asymmetric and non-indented model of the magnetopause location and shape. This model is obtained from fitting of 15 349 magnetopause crossings using 17 different spacecraft and is parametrized by the upstream solar wind dynamic and magnetic pressures, the IMF clock angle and the Earth dipole tilt angle. The constructed model provides a more accurate prediction of the magnetopause surface location than current Magnetopause surface models, especially on the night side of the magnetosphere.