Based on an expanded kinetic scheme for 32 subsequent and parallel reactions that yield linear polyurethane, a mathematical model was developed for a gradual polyaddition process involving toluene 2,4-diisocyanate and 1,4-butanediol. Unlike the earlier models, this one followed Flory＇s assumption and made the reactivities of the oligomers dependent solely on the chemical environment of their functional groups. Also, -NCO groups in this compound were considered to offer different chemical values. The model developed was presented in the form of a complex system of ordinary differential equations that describe changes in concentrations of both monomers, dimers, and oligomers making up the successive fractions of Linear polyurethane. Two essential kinetic constants for this model were calculated : the rate constant for the most reactive -NCO group within toluene 2,4-diisocyanate and the constant responsible for the substitution effect. At further stages, the model developed was subjected to experimental verification. Calculated number-average molecular weights of polyurethane were compared to gel permeation chromatography-determined values for sequenced steps of the polyaddition process conducted in chlorobenzene and tetrahydrofuran solvents, at temperatures of 86 degrees and 101 degrees C, and under conditions where diffusion effects could be neglected. The newly developed model was found to provide better fit for the process description as compared with the model that assumed the same rate constant at individual stages of the polyaddition process. However, the simulation results as compared with the so-called "quasioptimum" model, which assumed reactivities of oligomers to be dependent on their molecular weights, were in general inferior. The impact was discussed from the structures of reacting substances on their reactivities with the influences from other factors considered, too (e.g., the possibility of creating a system of hydrogen bonds can contribute to reactivity specifications of urethane oligomers with different molecular weights).