An analytical approximation is developed for the shape of the nightside tail current sheet, representing it as a function of the Earth's dipole tilt angle, solar wind ram pressure, and the interplanetary magnetic field (IMF). The model is based on 5-min average magnetometer data of the Geotail and Polar spacecraft, spanning the periods 1994--2002, and 1999--2001, respectively. All the magnetospheric data were tagged by concurrent values of the solar wind dynamic pressure and IMF By and Bz components, averaged over 30-min intervals immediately preceding the magnetospheric observations. Warping and twisting parameters were calculated by minimizing the number of mismatches between the observed and predicted orientation of the magnetic field on both sides of the model current sheet. The model is valid within the nightside magnetosphere in the range of tailward distances -50 RE ≤ XGSM ≤ 0. Variations of the solar wind pressure P change the shape of the deformed current sheet in such a way that an increase of P results in a decrease of the magnetotail hinging distance RH, but increases the magnitude of its transverse warping. The IMF Bz component affects the magnitude of the seasonal/diurnal motion of the current sheet in the north-south direction, and it also controls the degree of the IMF By-related twisting, which becomes much larger during the periods with northward IMF Bz.