To answer the increasing demand for electric power in Japan, Very Large Fast Reactors of 10,000 MWe unit capacity are expected to make their appearance in due course. The paper describes the method and results of a design study on a 10,000 MWe Liquid Metal Fast Breeder Reactor. First, a reference design was obtained for this unit of unprecedented capacity by extrapolating the various characteristics of a 1,000 MWe LMFBR and the nuclear characteristics thereof were studied. It was found that reactivity increase could be reduced to about 6 ¢ when seven subassemblies were voided in the central part of the core, and that the increase of reactivity and the decrease of breeding ratio with time were rather large for the initial loading core. Secondly, a design optimization procedure was developed based on complex method of nonlinear programming, and the method was applied to the Very Large Fast Reactor. The process resulted in a relatively large core height and fuel pin diameter, while the power cost was improve...