Three-dimensional continuous-energy coupled neutron-gamma Monte Carlo models of the Advanced Neutron Source (ANS) final preconceptual and conceptual reference core designs have been developed using the Monte Carlo Neutron and Photon transport code (MCNP) Version 3b. These models contain the reactor core with control rods, the heavy water reflector tank with shutdown rods and some beam tubes, and the outer light water pool. Eighty homogenized fuel zones per fuel element are used to represent the radial and axial 235U fuel distribution. These models are the most sophisticated, physically accurate reactor physics models of the ANS currently available. The use of MCNP methods and applications to the ANS are demonstrated. Beam tube studies, coolant voiding studies, and many criticality studies have already been performed, as have studies with variance reduction techniques. In comparison with deterministic methods, MCNP proves superior in calculating the core multiplication factor and neutron fluxes in the reflector. The MCNP code offers the ANS project the capability of performing complicated reactor physics calculations not currently possible with most deterministic methods.