We investigated the fault geometry effects and the corresponding coseismic slip distribution using various proposed earthquake fault models for the Chi-Chi earthquake of 21 September 1999. The types of fault geometries are threefold: a simple planar fault plane, a two segmented planar fault plane and a three dimensional (3D) curved fault surface rupture propagation model. We derived the estimated spatial slip distribution from an inversion analysis of GPS coseismic displacement data and show that the 3D fault model is the preferred solution. The simple and segmented fault models lead to significant artificial slip distributions associated with the pre-defined fault geometry and the spatial distribution of GPS stations. The spatial distribution of coseismic slip deduced from the 3D fault model has three observable features: (1) the overall slip is concentrated at depth of less than 12 km, which may well correspond to a shallow-dipping detachment; (2) the maximum slip of about 10 m is located 45 km to the north of the epicenter; and (3) the slip vector is dominated by the dip-slip component. In addition, the results from the inversion of GPS data are consistent with those from the inversion analysis of teleseismic broadband data. A resolution analysis, further, demonstrates that the results are highly correlated with field GPS data studies when we used synthetic test data. The inversion of spatially distributed GPS data is highly sensitive to fault geometry. We conclude that the use of the 3D fault model is not only necessary but also certainly competent enough to well explain the inferred slip style and the observed static coseismic displacements.