Soy protein elastomer (SPE) exhibits elastic, extensible, and sticky properties in its native state and displays great potential as an alternative to wheat gluten. The objective of this study was to better understand the roles of soy protein subunits (polypeptides) contributing to the functional properties of SPE. Six soy protein samples with different subunit compositions were prepared by extracting the proteins at various pH values on the basis of the different solubilities of conglycinin (7S) and glycinin (11S) globulins. Soy protein containing a large amount of high molecular weight aggregates formed from α' and α subunits exhibited stronger viscoelastic solid behavior than other soy protein samples in terms of dynamic elastic and viscous modules. Electrophoresis results revealed that these aggregates are mainly stabilized through disulfide bonds, which also contributed to higher denaturation enthalpy as characterized by DSC and larger size protein aggregates observed by TEM. Besides, the most viscoelastic soy protein sample exhibited flat and smooth surfaces of the protein particles as observed by SEM, whereas other samples had rough and porous particle surfaces. It was proposed that the ability of α' and α to form aggregates and the resultant proper protein-protein interaction in soy proteins are the critical contributions to the continuous network of SPE.