in many models for disperse two-phase flows, the pressure of the disperse phase is often assumed to be the same as that of the continuous phase, or differ only by an amount caused by the surface tension. This type of model is referred to as an equilibrium pressure model. Recent research indicates that the stress difference between the phases caused by dynamics of the motion can be significantly important in the modeling of disperse two-phase flows. Although this difference is still ignored in most calculations of disperse multiphase flows for various reasons, when an equilibrium pressure model is applied to continuous multiphase flows, a conceptual difficulty arises. For instance, the equilibrium pressure model cannot be used to study the tensile break of a sponge with interconnected pores, because the air in the pores can never go into tension while the sponge material does not break without tension. To avoid this conceptual difficulty, a multipressure model is introduced for continuous multiphase flows by analyzing and then modifying the implicit assumption about the volumetric strain rates involved in the equilibrium pressure model. Numerical implementations of the multipressure model are discussed. An example using the multipressure model is presented. Published by Elsevier Ltd.