A model is presented for free expansion polymer foam processing that includes simultaneous nucleation and bubble growth. The nucleation model includes dissolved gas, small critical cluster size, elastic, and non-ideal solution effects. An influence volume approach, which couples nucleation and bubble growth, is used to account for the limited supply of dissolved gas. The resulting set of equations are solved using a combination of numerical techniques. A parametric study Is conducted to examine the effects of key process variables on bubble growth, nucleation, and final bubble size distribution.