This paper describes the use of a CFD multiphase model using finite volume method, FLUENT, to aid understanding of the physical behaviour of solid and liquid flows in the digester of the pulping process. We take into consideration the mass balance of the multiinlets, outlets and circulation flows in the digester. We also look at the application of a porous media model to describe the dynamic behaviour of the liquor flow through a bed of solid particles. The cylindrical Korsnas/Vallvik pulping digester in Sweden is represented in the models as an axisymmetric two-dimensional model, which includes multiple feeds, outlets, pressure adjustment outflows and circulation pipes. Separation of the phases is an important part of the pulping process. A number of multiphase models are evaluated for their potential use in phase separation. For this evaluation we constructed the two-dimensional digester model in the Gambit software package, a preprocessor tool for FLUENT. Physical strainers at the entrances of outlet pipes were designed in Gambit, in order to investigate the possibility of physically separating large solid particles from the liquid flow where both phases are subject to suction into the circulation pipes. The compaction of the wood chips is also considered in the modelling. In the porous model, the digester is divided into sections of different porosity, and the behaviour of individual suspension particles is not considered. The bulk of this paper concerns modelling mass balances and phases of the mixture in the digester using Eulerian and mixture strategies.