Based on fine-resolution Geotail magnetometer data, a set of 5-min magnetic field averages was compiled for the period 1993-1997 and merged with 5-min average solar wind parameters, measured by IMP 8 and Wind spacecraft. Using this data set, the shape of the tail current sheet was studied in the interval -100 <X-GSM <-10 R-E as a function of the Earth's dipole tilt angle and of the By component of the IMF. The tilt-related warping of the current sheet and its twisting around the magnetotail axis in response to the IMF were modeled by analytical functions, whose parameters were found by least squares fitting to the data, for several bins of X-GSM A Similar modeling was also done for the near-tail region -20 <X-GSM <-10 R-E, using a set of 5-min ISEE 1/2 data, tagged by corresponding solar wind parameters from IMP 8, for the entire duration of the ISEE magnetometer experiment (1977-1987). The IMF-related twisting steadily increases down the tail and is quite conspicuous even at close geocentric distances (-20 less than or equal to X less than or equal to -10 R-E) A simple and flexible mathematical method is suggested, which allows quantitative modeling on a global scale of the IMF-related deformation of the cross-tail current by means of a "twist transformation" of the tail field. The method allows for a wide variety of possible geometries of the current sheet and keeps the total field confined within the magnetotail boundary. The results of the study are intended to be used in the development of an improved global model of the magnetospheric magnetic field, incorporating the effects of the IMF upon the magnetotail structure.