While recent geophysical measurements, including Global Positioning System (GPS) surveys, have clarified the mechanisms of active mountain building in the Taiwan arc-continent collision, the geometry of faults beneath the island remains unclear. In this paper we use GPS data collected before the 1999 Chi-Chi earthquake to image the geometry of active faults under Taiwan and estimate slip rates on these faults. We invert the data using kinematic and mechanical earthquake cycle models consisting of faulting in an elastic lithosphere overlying a viscoelastic asthenosphere. In the kinematic model, uniform slip is prescribed on the faults at a constant rate, while in the mechanical model, the faults slip in response to shear stresses in the lithosphere. These models explain the essential features of both the horizontal and vertical GPS velocity fields. We find a 27--39 km thick elastic lithosphere overlying a viscoelastic asthenosphere with Maxwell relaxation time of 15--80 years, or viscosity of 0.5--4 ¿ 1019 Pa s. The models produce a combined slip rate of 30--50 mm/yr on the frontal thrusts in western Taiwan and 60--80 mm/yr of slip on the Longitudinal Valley Fault. Inversion of the data using both models indicates a d¿collement dipping ~10¿ under western Taiwan and increasing in dip by no more than 10¿ under the Central Ranges and eastern Taiwan.