The time development of the polysaccharide content in the wood residue and the black liquor during kraft pulping for softwood is the focus of this study. The degradation process falls into two distinct categories: the chain element type and the chain fragment type. In the chain element reactions, a single element in the polymer chain can be removed, whereas in the chain fragment reaction a longer piece of the polymer is dissolved into the black liquor. The element-wise process consists of the subreactions peeling, stopping, and alkaline hydrolysis. A mathematical model considering peeling, stopping, and alkaline hydrolysis of the polymer chains as well as the dissolution of the wood components into the black liquor is presented and tested for the experimental data obtained from kraft cooking of Scots pine wood meal. As a novelty, the model distinguishes between primary peeling originating in the initial reducing end groups and secondary peeling following alkaline hydrolysis. Four series of cooking at high (1.55 M) hydroxide ion concentration were conducted at temperatures ranging from 130 to 160 degrees C. The reaction rates connected with the various processes were assumed to obey the Arrhenius equation, the frequency factor, and activation energy of which could be estimated while fitting the model to the data. Another series of cooking was executed at moderate (0.5 M) hydroxide ion concentration and at a temperature of 160 degrees C. The reaction rates associated with the different hydroxide ion concentrations were compared. Further, the effect of adding anthraquinone (AQ) to the cooking was modeled. The amounts of degradation attributed to the different subprocesses (primary peeling, secondary peeling, alkaline hydrolysis, and dissolution) were compared with each other for glucomannan, xylan, and cellulose.