This thesis is intended to improve the understanding of the role of die shape in promoting large volume expansion ratios of the extruded foams. It is important to control volume expansion in a foaming process since the ultimate purpose of any foam process is to produce foams having a desirable expansion ratio. Control of volume expansion is also important to increase the efficiency of the costly (and often times hazardous) blowing agent. In foam extrusion, the die geometry affects cell nucleation, growth and shaping. In other words, the die geometry, in addition to the processing conditions and material properties, plays a critical role in determining the volume expansion ratio of the extruded foams. The final volume expansion ratio of the extruded foams blown with a physical blowing agent (PBA) is mainly governed by the loss of the blowing agent through the foam skin. In this thesis, fundamental studies were conducted to simulate gas loss, cell nucleation, and premature cell growth that occurs inside an extrusion die. Then, the effect of the die geometry on gas loss and volume expansion was theoretically analyzed. The study shows that the die geometry affects the final volume expansion ratio of extruded foams mainly through the amount of premature cell growth and the number of cell layers across the foam thickness. A large amount of premature cell growth will lead to an initial hump at the die exit and reduce the cell wall thickness. Consequently, gas loss will be accelerated. When the amount of premature cell growth exceeds some critical value, the expansion ratios will be dramatically decreased, even at the optimum temperature. An increased number of cell layers across the foam thickness will suppress gas loss by localizing gas loss to the surface layers, and as a result, cells in the inner layers can fully grow and volume expansion will be promoted. The developed concept was verified by using convergent-filamentary and annular dies with various geometries. Finally, a fundamental study of bubble growth and collapse under atmospheric pressure with a chemical blowing agent (CBA) was also conducted.