A mathematical model was developed for plasticating single-screw extrusion of amorphous polymers. We considered a standard metering screw design. By introducing a ’critical flow temperature’ (T-cf), below which an amorphous polymer may be regarded as a ’rubber-like’ solid, we modified the Lee-Han melting model, which had been developed earlier for the extrusion of crystalline polymers, to model the flow of an amorphous polymer in the screw channel. T-cf is de facto a temperature equivalent to the melting point of a crystalline polymer. The introduction of T-cf was necessary for defining the interface between the solid bed and the melt pool, and between the solid bed and thin melt films surrounding the solid bed. We found from numerical simulations that (1) when the T-cf was assumed to be close to its glass transition temperature (T-g), the viscosity of the polymer became so high that no numerical solutions of the system of equations could be obtained, and (2) when the value of T-cf was assumed to be much higher than T-g, the extrusion pressure did not develop inside the screw channel, Thus, an optimum modeling value of T-cf appears to exist, enabling us to predict pressure profiles along the extruder axis. We found that for both polystyrene and polycarbonate, T-cf lies about 55 degrees C above their respective T(g)s. In carrying out the numerical simulation we employed (1) the WLF equation to describe the temperature dependence of the shear modulus of the bulk solid bed at temperatures between T-g and T-cf, (2) the WLF equation to describe the temperature dependence of the viscosity of molten polymer at temperatures between T-cf and T-g + 100 degrees C, (3) the Arrhenius relationship to describe tile temperature dependence of the viscosity of molten polymer at temperatures above T-g 100 degrees C, and (4) the truncated power-law model to describe the shear-rate dependence of the viscosity of molten polymer. We have shown that the T-g of an amorphous polymer cannot be regarded as being equal to the T-m of a crystalline polymer, because the viscosities of an amorphous polymer at or near its T-g are too large to flow like a crystalline polymer above its T-m. Also conducted was an experimental study for polystyrene and polycarbonate, using both a standard metering screw and a barrier screw design having a length-to-diameter ratio of 24. For the study, nine pressure transducers were mounted on the barrel along the extruder axis, and the pressure signal patterns and axial pressure profiles were measured at various screw speeds, throughputs, and head pressures. In addition to significantly higher rates, we found that the barrier screw design gives rise to much more stable pressure signals, thus minimizing surging, than the metering screw design. The experimentally measured axial pressure profiles were compared with prediction.