The geological setting of southwestern Oklahoma and northeastern Texas is an ideal example of an aulacogen, the result of the tectonic evolution of a failed rift of the North American continent during the Palaeozoic era (540-360 Ma). The Wichita Province forms the uplifted basement portion of this Southern Oklahoma Aulacogen (SOA). The major fault zones to its north and south are clearly evident in gravity gradient maps produced by the recently constructed Earth Gravitational Model 2008 (EGM2008). Fault parameters, such as the dip angle, location and density contrasts have been estimated from profiles of seismic data and local gravimetry in the 1990s. On the other hand, gravitational gradients that are derived from EGM2008 and then combined to form the differential field curvature are particularly indicative of linear structures such as dip-slip faults. They are used here exclusively, that is, without additional geophysical constraints, in an optimal, least-squares estimation based on the Monte Carlo technique of simulated annealing to determine dip angle and location parameters of the major faults that border the Wichita Uplift region. Results show that these faults have small dip angles, in basic agreement with the low-angle faults inferred from seismic studies. The EGM2008 gradients also appear in some cases to provide an improved map of the major faults in the region, thus offering a strong constraint on their location.