Direct body waves and fundamental surface waves are calculated for a credible, hypothetical great earthquake on the San Andreas Fault. The prototype event assumed is the Fort Tejon earthquake of January 9, 1857. Amplitudes and durations of long-period ground motion (T > 1 sec) are found for a receiver in downtown Los Angeles. Calculations are carried out for various epicenters, dislocation profiles, and time functions. Ground motion from Love radiation is found to be most important, with peak-to-peak amplitudes up to 14 cm and durations up to 5 min. This duration is a factor of 3 longer than has been assumed by previous design earthquakes whose estimates have been based upon acceleration criteria. Although the present result reveals several important features of long-period ground motion resulting from a great earthquake, more details of rupture propagation need to be known before a more definitive prediction can be made. The present result should be considered tentative.