The molecular cluster model for homogeneous bubble nucleation was extended to predict the bubble nucleation events in elastomers, polymers and polymer solutions. For nucleation in elastomers and polymers, the strain energy overcome by a critical bubble during growth period was also considered. The calculation results for the number of bubbles nucleated are in good agreement with observed results. Further, the growing of the critical bubble by the diffusion process in a viscoelastic medium was treated by an integral method for the concentration boundary layer. The calculated cell sizes depending on the initial saturation pressure are in close agreement with the observed sizes. The governing equations developed in this study may be used in polymer processing of microcellular foams. (C) 2004 Society of Plastics Engineers.