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Mono Lake, California is a perennial, closed-basin saline lake. Up to 2 km of sediments have accumulated below the lake, and a well log shows that saline groundwater of concentration > 18,000 ppm extends to the bottom of the basin fill. We investigated the groundwater system with the variable-density flow and solute transport code SUTRA to determine if the basin's recharge and inferred groundwater salinity are consistent with observational data. Steady state model predictions of the position and shape of the interface separating saline from fresh groundwater are consistent with the salinity profile derived from the spontaneous-potential (SP) log of a geothermal well on the lake's shoreline. We also inferred the basin-wide saline groundwater distribution and concentration from experiments with a steady state model of the entire basin groundwater system. Hydrologic variations around the lake determine the position of the saline-fresh groundwater interface: Higher recharge rates characteristic of the Sierra Nevada shoreline push the interface far beneath the lake. The interface probably lies below the shoreline around much of the rest of the lake. On the low-recharge northeastern shoreline the interface top may lie outside the lake edge. This positions the saline groundwater discharge zone just below the playa surface and contributes to development of salt flats on the recently exposed former lake bed. Simulations suggest that the basin fill permeability may not have significant anisotropy, possibly owing to extensive faulting which increases vertical permeability. For an anisotropic basin fill, the resultant increased channeling of recharge beneath the lake readily overcomes the opposing force of the saline groundwater density, and it is flushed out of the basin sediments. A simple permeability representation of the basin lithology, with low permeability below the lake and an anisotropic transition to higher permeability outside the lake, reasonably represents the well and spring water salinity observations.