A model for investigating the melting process of polymer in a vibration-induced single-screw (VISS) extruder is presented. The key feature of this model is as follows: vibration force field is introduced into the overall course of extrusion by the axial vibration of the screw, and the velocity distribution in the polymer melt behaves strongly nonlinear and time-dependent. To analyze this model, half-open barrel visible experimental method and low-density polyethylene material are adopted to investigate the effect of the vibration parameters on the melting process, which goes into further details of study and research on the melting mechanism, and thus, a novel physical melting model is derived. Combining the conservation equations of mass, movement, energy, and constitutive, analytical expressions of the melting rate, the energy consumption, the length of melting section, and the distribution of solid bed are obtained. This model enables the prediction of the processing and design parameters in the VISS extruders from which the optimum conditions for designing VISS extruder and polymer processing are obtained. The theory is supplemented by a calculation sample and experiment, which shows that the introduction of vibration force field can improve the melting capacity and decrease the power consumption of extruder greatly. (c) 2006 Wiley Periodicals, Inc. J Appl Polyrn Sci 100: 3860-3876, 2006.