The rheological properties of conventional polyethylene terephthalate (PET) resins are not particularly suitable for low density extrusion foaming with physical blowing agents; as a result, chemically modified resins through chain extension/branching reactions are often used. Such resins have overall higher melt viscosity and higher melt strength/melt "elasticity" than unmodified materials. In this work, following a review of the prior art on PET chemical modification, an unmodified and a chemically modified resin were selected and characterized for their melt viscoelastic properties including shear and dynamic complex viscosity over a broad shear rate/frequency range, storage and loss modulus, and die swell. Certain rheological models were found to provide better fits of the entire viscosity curve for the unmodified vs. the modified resin. Foamed extrudates having variable densities (from about 1.2 to 0.2 g/cc), were prepared by carbon dioxide injection in monolayer flat sheet extrusion equipment. Foams with increasingly lower density, below 0.5 g/cc, were obtained by increasing gas pressure only in the case of the chemically modified resin. The effects of variables such as concentration of the physical blowing agent, resin rheology, resin thermal properties and choice of process conditions are related to product characteristics including density, cell size and crystallinity.