A mathematical model was developed to analyze the continuous stepwise polymerization of polyol and diisocyanate to form the thermoplastic polyurethane in a single-screw extruder. The reactants used in this system wert MDI, 1, 4-butanediol and poly(caprolactone glycol) (M.W. 832) with equivalent weight ratio of 2:1:1. The reaction kinetics and the viscosity function were obtained through experiments and the balance equations of chemical species, momentum and energy in rectangular coordinates were established for an unwound channel. These equations were solved numerically to calculate the velocity, residence time, conversion, temperature and pressure profiles at various operating conditions. The effect of T_b/T_s ratio, RPM and catalyst concentration were discussed.