The theoretical and computational bases of the BACCHUS-3D/TP computer program are reviewed. The computer program has been developed in the frame of the liquid-metal fast breeder reactor safety project at the Kernforschungszentrum Karlsruhe and is used for thermal-hydraulic analyses of nuclear fuel bundles under normal and accident conditions. The present program combines two models and solution procedures previously used separately, namely, an improved slip model and a separated-phases model. The first model uses mixture equations and accounts for slip between the phases, whereas the latter uses separate continuity and momentum equations. At the present stage of development, both assume thermodynamic equilibrium. Techniques used to affect smooth transitions between the two models are described, including treatment of frictional pressure drop and solution of the Poisson pressure and momentum equations. A detailed derivation of the computation of mass transfer between the phases is given because it is a central and novel feature of the model. A summary of validations performed to date, together with the quantities measured and compared with computations is given in tabular form.