A simulation of simultaneous bubble nucleation and growth was performed for a batch physical foaming process of polypropylene (PP)/CO2 system under finite pressure release rate. In the batch physical foaming process, CO2 gas is dissolved in a polymer matrix under pressure. Then, the dissolved CO2 in the polymer matrix becomes supersaturated when the pressure is released. A certain degree of supersaturation produces CO2 bubbles in the polymer matrix. Bubbles are expanded by diffusion of the dissolved CO2 into the bubbles. The pressure release rate is one of the control factors determining number density of bubbles and bubble growth rate. To study the effect of pressure release rate on foaming, this paper developed a simple kinetic model for the creation and expansion of bubbles based on the model of Flumerfelt's group, established in 1996 [Shafi, M.A., Lee, J.G., Flumerfelt, R.W., 1996. Prediction of cellular structure in free expansion polymer foam processing. Polymer Engineering and Science 36, 1950-1959]. It was revised according to the kinetic experimental data on the creation and expansion of bubbles under a finite pressure release rate. The model involved a bubble nucleation rate equation for bubble creation and a set of bubble growth rate equations for bubble expansion. The calculated results of the number density of bubbles and bubble growth rate agreed well with experimental results. The number density of bubbles increased with an increase in the pressure release rate. Simulation results indicated that the maximum bubble nucleation rate is determined by the balance between the pressure release rate and the consumption rate of the physical foaming agent by the growing bubbles. The bubble growth rate also increased with an increase in the pressure release rate. Viscosity-controlled and diffusion-controlled periods exist between the bubble nucleation and coalescence periods. (c) 2008 Elsevier Ltd. All rights reserved.