Geodetic arrays observed by the U.S. Coast and Geodetic Survey span the Imperial fault in southern California. For the 1940 M 7.1 Imperial Valley earthquake, a 1934--1941 triangulation network has sufficient resolution to allow inversion for the coseismic slip distribution on fault segments 5 to 25 km long extending from the surface to a depth of 9 km. The estimated right-lateral slip is 0.8 to 1.7 m on the northern 30 km of the main trace of the Imperial fault, 4.8¿0.2 m on a 10-km-long segment straddling the United States-Mexico border, and 1.3¿0.4 m on a southern 25-km-long segment in Mexico. Fixing this strike-slip model and inverting 1940 leveling data only for dip slip yields 0.1 m of east-side-down dip slip. The seismic moment for this model is M0=(3.2¿0.3)¿1019 N m. The 1979 geodetic data set, mostly elevation changes from leveling routes, has insufficient resolution for inversion. However, it is possible to use this geodetic data set and results published by others to infer that the 1940 and 1979 earthquakes may be similar on the rupture zone common to both events. Our preferred 1940 model is similar to the 1979 geodetic results of Crook <1984> on the segments where both networks have good resolution. Elevation changes from 1940 and 1979 leveling data are very similar. Thus the geodetic data corroborate the surface slip evidence of Sharp <1982b> that the 1940 and 1979 slip distributions are examples of characteristic slip on the northern Imperial fault. ¿ 1998 American Geophysical Union