During the interseismic phase of the earthquake cycle, between large earthquakes, stress on faults evolves in response to elastic strain accumulation driven by tectonic plate motions. Because earthquake cycle processes induce non-local stress changes, the interseismic stress accumulation rate on one fault is influenced by the behavior of all nearby faults. Using a geodetically constrained block model, we show that the total interseismic elastic strain field generated by fault interactions within Southern California may increase stressing rates on the Mojave and San Bernardino sections of the San Andreas fault within the Big Bend region by as much as 38% relative to estimates from isolated San Andreas models. Assuming steady fault system behavior since the C.E. 1857 Fort Tejon earthquake, shear stress accumulated on these sections due only to interaction with faults other than the San Andreas reaches 1 MPa, ∼3 times larger than the coseismic and postseismic stress changes induced by recent Southern California earthquakes. Stress increases along Big Bend sections coincide with the greatest earthquake frequency inferred from a 1500-yr-long paleoseismic record and may affect earthquake recurrence intervals within geometrically complex fault systems, including the sections of the San Andreas fault closest to metropolitan Los Angeles.