Phase equilibrium calculation involving VLLE is often encountered in design, simulation and optimisation of many chemical processes. Practically, VLLE is numerically solved by a set of equations of chemical potential equilibrium and mass balances, which in theory may lead to multiple solutions due to the high nonlinearity of equations. Here, the multiplicity of VLLE is analysed by continuation method with pressure and composition as parameters. The detailed features of the output multiplicity of VLLE, e.g. the multiple liquid compositions and relative holdups, multiple liquid-liquid boundaries as well as the mixture composition region resulting in multiplicity, are presented. The influence of VLLE on process multiplicity is illustrated through the flash process. Moreover, the effect of the activity model is investigated, which shows that multiplicity of VLLE may change significantly and even disappear using different activity models. The multiplicity study of the VLLE problem is very helpful for evaluating the activity models and parameters and for providing proper initial values for simulation of system with VLLE multiplicity. (c) 2006 Elsevier Ltd. All fights reserved.