By reactive extrusion with pyromellitic dianhydride (PMDA), foamable poly(ethylene terephthalate) (PET) was obtained, which achieved a maximum intrinsic viscosity of 1.36 dL/g with PMDA content 0.8 wt%. Dynamic shear rheological properties were measured to characterize the structure evolution of modified PET. And the Avrami analysis was extended for the non-isothermal crystallization process of modified PET, which relates to cell stabilization in the melt foaming process. Based on the batch foaming process with supercritical carbon dioxide as blowing agent, broad foaming temperature windows were obtained for PETs modified with 0.8 and 0.5 wt% PMDA, in which PET foams with the expansion ratio between 10 and 50 times, the cell diameter between 15 and 37 m, and the cell density between 6.2 x 10(8) and 1.6 x 10(9) cells/cm(3) were controllably produced. POLYM. ENG. SCI., 55:1528-1535, 2015. (c) 2014 Society of Plastics Engineers