Styrene–ethylene–butylene–styrene and its blends containing 10, 30 and 50 wt% polystyrene were subjected to batch foaming using physical blowing agent carbon dioxide. At higher foaming temperatures (80–110℃), complex viscosity (*) and storage modulus (E') were found to control the volume expansion ratio and the shrinkage of foams. For a given composition, optimal volume expansion was achieved at temperatures close to the glass transition temperature (T _g ) of the polystyrene phase of that composition, indicating the presence of a complex viscosity window favourable for the foaming process. Blends with 30% and 50% polystyrene content possessed higher values of E' and *, and produced stable foams having higher volume expansion ratio, when foamed within their respective * windows. At a much lower foaming temperature (35℃), polystyrene was found to have a nucleating effect. However, irrespective of rheological properties, all foams showed prominent shrinkage. A higher polystyrene content resulted in a lower volume expansion ratio, as well as shrinkage over a shorter period of time and a greater extent of shrinkage in the same time span. This can be attributed to the selective foaming of the ethylene–butylene phase, hindered by the stiff polystyrene aggregates.