A method for designing and optimizing recirculating pebble-bed reactor cores is presented. At the heart of the method is a new reactor physics computer code, PEBBED, which accurately and efficiently computes the neutronic and material properties of the asymptotic (equilibrium) fuel cycle. This core state is shown to be unique for a given core geometry, power level, discharge burnup, and fuel circulation policy. Fuel circulation in the pebble-bed can be described in terms of a few well-defined parameters and expressed as a recirculation matrix. The implementation of a few heat-transfer relations suitable for high-temperature gas-cooled reactors allows for the rapid estimation of thermal properties critical for safe operation. Thus, modeling and design optimization of a given pebble-bed core can be performed quickly and efficiently via the manipulation of a limited number key parameters. Automation of the optimization process is achieved by manipulation of these parameters using a genetic algorithm. The end result is an economical, passively safe, proliferation-resistant nuclear power plant. iv