The major difficulty in the design of control and operating systems for Kamyr Digesters in Kraft pulp mills has been the lack of a suitable chemical kinetic and process dynamic mathematical model. In addition, little use has been made in the past of the available new techniques in automatic control system design.This paper presents a new and more powerful mathematical descriptive model of the Kraft pulping process. Included also are representations of some of the most important fluid dynamics parameters. Both can be used to help evaluate potential control systems for the process.The model developed accounts for alkali pulping with or without the presence of sulfide. It also contains terns describing the degradation of the wood cellulose. In addition, it contains functions giving representations of process yield and process K number or an analytic representation of the extent of lignin extraction.