Abstract: Based on the T96 model, we obtained the topology of the Earth's cusp and defined some parameters (e.g., minimum magnetic latitude of the equatorial boundary, latitudinal width, flare angels in the meridian and terminator plane, inclination, flatness, central magnetic local time) to describe its configuration. The influences of the solar wind dynamic pressure, the interplanetary magnetic field and storm intensity on the cusp's configuration are further studied. As the increasing of the solar wind dynamic pressure and storm intensity, the cusp's minimum magnetic latitude of the equatorial boundary, inclination, and the flatness all decrease, while the latitudinal width and flare angles in the midnight-noon and dawn-dusk directions increase. With the increasing of southward IMF, the equatorial boundary, latitudinal width, flare angle in the midnight-noon direction and inclination all decrease, while the flare angle in the dawn-dusk direction and flatness both increase. However, the situations of northward IMF are contrary. The magnetic local time of the cusp is controlled by IMF B_y. When B_y is positive/negative, the cusp moves toward dusk/dawn side. And there is a good linear correlation between the magnetic local time and IMF B_y. By comparing to some former observational results, the cusp obtained from the T96 model is nearly in accordance with the observations.