We describe a simple method to determine the probability distribution function of the magnitudeMmax and return period TR of the maximum plausible earthquake on crustal faults. The method requires the background seismicity rate (estimated from instrumental data) and the rate of interseismic moment buildup. The method assumes that the moment released by the seismic slip is in balance with the moment deficit accumulated in between earthquakes. It also assumes that the seismicity obeys the Gutenberg-Richter (GR) law up to Mmax. We took into account the aftershocks of large infrequent events that were not represented in the instrumental record, so that we could estimate the average seismicity rate over the entire fault history.We extrapolated the instrumental record, using the GR law to model the frequency of larger events and their aftershocks. This increased the frequencies of smaller events on average; when these smaller events were newly extrapolated, they predicted a higher frequency of larger events. We iterated this process until stability was reached, and then we assumed moment balance when we found the maximum magnitude; we have found this method to be appropriate in applications involving examples of fault with good historical catalogs. We then showed examples of applications to faults with no historical catalogs. We present results from nine cases. For the San Andreas fault system, we find Mmax = 8:1 ± 0:3, with TR380950120 yrs; for the North Anatolian fault, Mmax = 8:0 ± 0:3, with TR275650135 yrs; for the Main Himalayan thrust, Mmax = 9:0 ± 0:2, with TR12002700550 yrs; for the Japan trench, Mmax = 9:3 ± 0:3, with TR5201200220 yrs; for the Sumatra-Andaman trench, Mmax = 9:0 ± 0:3, with TR20045080 yrs; for the Boconó fault, Mmax = 7:3 ± 0:3, with TR16036070 yrs; for the Altyn Tagh fault, Mmax = 8:0 ± 0:3, with TR9002000400 yrs; for the Dead Sea Transform, Mmax = 7:8 ± 0:3, with TR10002400450 yrs; and for the Kunlun fault, Mmax = 8:0 ± 0:3, with TR10002000450 yrs.