The strength of vibration welds of thermoplastics is governed by the weld zone microstructure, which in turn, is closely tied to the welding process variables, such as the thickness of the weld melt film and the temperature profiles therein. The mathematical model described in this report is aimed at describing the role of the rheology of the melt-specifically the magnitude and shear rate dependence of the melt viscosity-in governing the melt film variables during the steady state penetration phase (Phase III) of vibration welding. The steady state momentum balance and heat transfer within the melt film are solved by using the power law model for viscosity. Closed-form analytical expressions are obtained for estimating the melt film thickness, the shear rates, and the temperature field within the film. This model has been used to estimate weld zone variables for four different polymers displaying a wide range of viscosities and shear thinning behaviors. POLYM. ENG. SCI., 54:499-511, 2014. (c) 2013 Society of Plastics Engineers