The transient simulation of a liquid-metal fast breeder reactor (LMFBR) plant requires (a) modeling of all processes that may be encountered and (b) the development of numerical methods to solve them. All models needed for the thermohydraulic simulation of the whole plant are formulated in this paper. We examine numerical techniques required to solve the governing equations, which are hyperbolic and parabolic partial-differential equations and ordinary differential equations. It appears that the implicit (or partially implicit) scheme is most suitable to meet both the stability and accuracy requirements. A new approach, labeled as the multistep scheme, to efficiently solve the entire system is then presented and illustrated through an example. For a simplified test problem, the multistep scheme has been found to be more efficient (by a factor of 2 to 3) than the commonly used single-step methods. This effort has resulted in the creation of a system transient simulation code, called SSC, for LMFBRs.