Ground deformation and seismicity observed from 1975 to the present support the existence of magma beneath the central part of Long Valley caldera, California. Constraints on the source geometry are obtained from deformation modeling of uplift and trilateration data over the period 1975--1982. The deformation data are modeled with an elastic half-space incorporating an ellipsoidally shaped magma chamber under uniform pressure, the Hilton Creek fault, and the South Moat fault. The best fit to the deformation data indicates a nearly spherically shaped source beneath the central part of the caldera at a depth of 9.5¿1 km. However, significant deviations of some horizontal displacement data suggest that movements along the faults are probably more complicated than the assumed dislocations. The predicted normal stress on the vertical South Moat fault plane varies from weak tension above 4 km depth to strong compression below that depth and the shear stress is right-lateral in the eastern half and left-lateral in the western half of the fault. It is unlikely that such a stress field could trigger slip movement on the fault. Tangential stress at the surface of the magma chamber has a maximum tension near its intersection with the South Moat fault. It is possible that the 1983 earthquake swarms in the South moat were triggered by shallow magma intrusions beneath the South Moat of the caldera. A narow prolate ellipsoidal source, which produces about the same uplift as the spherical source model, leads to a horizontal tensile stress that is about 1 order of magnitude higher in the region directly above the source. However, the crack opening location for magma injection is at the top of the source in this case and would not be related to the seismicity in 1983. ¿ American Geophysical Union 1988