In this study three different modeling approaches, with varying levels of sophistication and complexity, on modeling kraft cooking kinetics have been investigated. In the first and second approaches, isothermal conditions were used by converting the heating and cooling times into isothermal time. In the third approach, real temperature and time were used. Donnan theory, accounting for the cation exchange property of the wood fibers, was used in the second and third approaches for estimation of the cooking chemical concentrations in the fiber wall liquid, whereas in the first approach the cooking chemical concentrations in the bulk liquid phase were used. A modification of the Purdue model was used for modeling the delignification kinetics. The parameters of the Purdue model were regressed both with Matlab (commercial software) and Kinfit (in-house software). All three regressions with different modeling approaches provided very good fits to the experimental data. When Donnan theory and real temperature profiles (third approach) were employed, the estimated reaction rates for the faster reacting lignin subcomponent in the Purdue model decreased at all temperatures. On the other hand, the portion of the faster reacting component increased from 24% to 28%. In this way the third modeling approach mimics the reality in the most accurate way. Its implementation is more tedious, but the model should have more predictive capabilities. Furthermore, the effect of anthraquinone on kraft cooking kinetics was studied.