On the basis of the gradual polyaddition kinetic model developed earlier, an attempt was made to provide a generalized mathematical model for the set of reactions yielding linear polyurethanes. The model is a system of first-order ordinary differential equations. It was assumed at the present stage of this model that the rate constants for the reaction considered do not change. The model developed was then solved numerically Average molecular weight of the polymer and composition data for oligomers were calculated for a constant volume batch reactor and varied process parameters. The GPC method, which was tested for model urethane oligomers, was employed to verify the model developed. The reaction of 2,4-TDI with 1,4-butanediol proceeding in a solution was investigated. It was concluded that the model was applicable to a limited degree in describing the linear polyurethane manufacturing process which is more complex. However, it was suggested that the algorithms adopted could be utilized in developing further models which could assume changing rate constants for the polymer chain growth reactions.