An improved quantitative representation of the magnetic field in the geomagnetosphere is developed. The model takes into account the effect of warping the tail current sheet in two dimensions due to the geodipole tilt, as well as spatial variations of the current sheet thickness along the Sun-Earth and dawn-dusk directions. The corresponding analytic forms for the magnetic field components have been obtained using an indirect approach in a two-stage procedure. First of all, a simple axially symmetric infinitely thin current disc model with different rates of the current density decreasing in the radial direction are derived. The next step consists in a formal modification of the obtained expressions for the vector potential, which results in a transverse broadening of the initially thin current sheet and incorporates an account for the sheet warping. A truncation factor is also introduced, with the aim to simulate the finite extension of the current system in the dawn-dusk direction, as well as its day-night asymmetry. Based on the proposed representation and the IMP and HEOS spacecraft data pool, a series of magnetospheric models are generated, giving a quantitative description of the average magnetic field configuration for different disturbance levels. A comparison of the magnetic field distributions predicted by the model and those measured at geosynchronous orbit has been carried out.