Abstract Quality and economical requirements have raised evident need and interest in the industry to further develop continuous kraft cooking. A Kappa number, representing the cooking degree, is one of the few quality measures of cooking, and usually the only one measured on-line. Cooking degree is mainly controlled by temperature, chemical charge, and cooking time. Cooking conditions strongly depend on the packing degree of a chip column in the digester. At the same time, the packing of a chip column is affected by the cooking degree of chips. A typical problem is that the conditions and cooking degree in the process are not known. To achieve better control, more information about the cooking process is required. The aim of this thesis has been to more accurately describe the cooking conditions and phenomena in the digester scale. Conventional and Downflow Lo-Solids™ continuous cooking processes, producing both softwood and hardwood pulp, were investigated. Information achieved from measurements, and physical and chemical models describing chip scale phenomena, were utilised. Kappa number modelling was based on the use of an optimised and on-line adapted Gustafson's model. Modelling over grade change situations was accomplished by smoothly adjusting the model parameters as a function of temperature change profiles. Real-time profiles of cooking chemicals, temperature, and lignin and carbohydrates contents of chips within the processes were modelled. These real-time profiles were utilised in the modelling of the chip column's packing degree in the conventional process. Based on the developed models, blow-line Kappa numbers of both processes were predicted. By exploiting the prediction results, a new control strategy for the Kappa number was developed. In the strategy, set points for chemical charge and cooking temperature are iteratively solved by using only the developed prediction models of the blow-line Kappa number. It was shown that the modelled profiles of wood components and cooking chemicals can give new information regarding the continuous cooking processes. The modelling results are feasible in control purposes, and they also can support the operators' work. In the new control strategy, compared to the widely used H-factor based control, chemical concentrations can be more precisely taken into account.