Geodetic data show that the Los Angeles metropolitan area is undergoing 8–9 mm/year of north‐south tectonic shortening associated with the Big Bend of the San Andreas Fault. This shortening has been linked to multiple damaging twentieth century thrust earthquakes as well as possible Mw ≥ 7.0 Holocene thrust events beneath central Los Angeles. To better characterize this seismic hazard, we assess how this shortening is being accommodated by interseismic strain accumulation on subsurface faults, incorporating detailed seismology‐ and geology‐based models of fault geometry and the low‐stiffness Los Angeles sedimentary basin. We find that strain accumulation on local strike‐slip faults likely contributes no more than 1–2 mm/year of the shortening. We formally invert the geodetic data for the pattern of interseismic strain accumulation on the north dipping Sierra Madre, Puente Hills, and Compton thrust faults and a master decollement. We explore the impact of the assumed material model, strain accumulation on faults to the west and east, and other model assumptions. We infer that the three faults slip at 3–4 mm/year over the long term and are currently partially or fully locked and accruing interseismic strain on their upper sections. This locking implies an annual deficit of seismic moment, 1.6 + 1.3/−0.5 × 1017 Nm/year in total, which is presumably balanced over the long‐term average by the moment released in earthquakes. The depth distribution of moment deficit accumulation rate matches that of seismicity rates in Los Angeles to first order, in part, because the models incorporate the blind nature of the Puente Hills and Compton Faults.