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Chemical interactions between the fibers of cellulose and liquor flow in a continuous pulping digester were modeled using CFD, (Computational Fluid Dynamic) and the finite volume method (FVM). A 2D geometric representation of the digester was constructed in Gambit. The total volume of the reactor was considered using the axisymmetric function of FLUENT. CFD is a numerical solution method of PDE (Partial Differential Equations) in many different control volumes such as pipes, reactors, vessels or any component. Differential form of the conservation equations of mass, momentum and energy (including the chemical reactions) are solved using the CFD codes. In order to avoid complications arising from instability and divergence, the circulation flows around the digester were ignored. The calculations were performed for the pulping of softwood chips. In order to model the kinetics of the pulping reactions, the chemical reactions of the fibers were calculated theoretically and the Arrhenius constants for the reactions were computed. The activation energy was also calculated according to data provided for the cooking conditions. The stoichiometry of the reaction equation was determined from the operational data of the cooking process. The stoichiometry and Arrhenius parameters were prescribed by CFD codes in order to characterize the pulping chemical reactions in the digester. The reaction was modeled under isothermal conditions. The species transport and reaction scheme were incorporated with a homogeneous porous media to represent compaction of the fibers in the digester. The progress of the reaction represents the quantitative development of the pulping process. However, the qualitative progress is controlled by the stoichiometry of the reaction. This means that a good model of the reaction stoichiometry can ensure continuous production of high quality pulp.