The thickness of the melt film and the temperature profiles within the melt film in the weld zone are key process variables governing the development of weld-zone microstructures and the resulting development of weld strengths, during vibration welding of thermoplastics. The mathematical model described in this report is aimed at investigating the role of the rheology of the meltspecifically the magnitude and shear-rate as well as temperature dependence of the melt viscosityin governing the process variables such as the molten film thickness and the viscosities, stresses, and the temperatures within the melt film during vibration welding. The analysis is focused on the steady-state penetration phase (phase III) of vibration welding. The coupled steady-state momentum balance and heat transfer within the melt film, formulated using the Cross-WLF (Williams-Landel-Ferry) relationship for viscosity, are solved in an iterative finite element framework. The model has been implemented for two different polymers displaying significant differences in viscosities and shear thinning behaviors. An attempt has been made to correlate the trends in the estimated melt film variables with the experimentally measured weld quality. POLYM. ENG. SCI., 2012. (c) 2011 Society of Plastics Engineers