This paper describes the basic equations and solution techniques of a collection of heat transfer and coolant voiding dynamics models that have been developed and successfully applied to simulate hypothetical accidents in liquid-metal-cooled fast breeder reactors (LMFBRs) to the point of permanent subcriticality or to the initiation of a prompt-critical excursion. These models emphasize analytic and integral solution techniques to minimize computational time and have been programmed into the SACO fast-running accident analysis computer code. The comparisons of SACO results to analogous SAS3D results used to qualify these models are illustrated and discussed. The fast-running nature of these models makes them an ideal sensitivity analysis tool for use in probabilistic evaluations of LMFBR accidents. Their use in this application is illustrated.