The locked section of the San Andreas fault in southern California has experienced a number of large and great earthquakes in the past, and thus is expected to have more in the future. To estimate the location, time, and slip of the next few earthquakes, an earthquake instability model is formulated. The model is similar to one recently developed for moderate earthquakes on the San Andreas fault near Parkfield, California. In both models, unstable faulting (the earthquake analog) is caused by failure of all or part of a patch of brittle, strain-softening fault zone. In the present model the patch extends downward from the ground surface to about 12 km depth, and extends 500 km along strike from Parkfield to the Salton Sea. The variation of patch strength along strike is adjusted by trial until the computed sequence of instabilities matches the sequence of large and great earthquakes since a.d. 1080 reported by Sieh and others. The last earthquake was the M=8.3 Ft. Tejon event in 1857. The resulting strength variation has five contiguous sections of alternately low and high strength. From north to south, the approximate locations of the sections are: (1) Parkfield to Bitterwater Valley, (2) Bitterwater Valley to Lake Hughes, (3) Lake Hughes to San Bernardino, (4) San Bernardino to Palm Springs, and (5) Palm Springs to the Salton Sea. Sections 1, 3, and 5 have strengths between 53 and 88 bars; sections 2 and 4 have strengths between 164 and 193 bars. Patch section ends and unstable rupture ends usually coincide, although one or more adjacent patch sections may fail unstably at once. The model predicts that the next sections of the fault to slip unstably will be 1, 3, and 5; the order and dates depend on the assumed length of an earthquake rupture in about 1700. ?? 1985 Birkha??user Verlag.