Expandable, rubber-modified styrene polymers for elastic polystyrene foams comprisea) a continuous phase comprising polystyrene or a styrene copolymer containing at most 50% of copolymerized comonomers andb) from 5 to 30% by weight of a butadiene-styrene block copolymer dispersed therein,and also a low-boiling blowing agent. The rubber particles have a compact lamellar structure without polystyrene inclusions. The expandable styrene polymers are prepared by polymerization of styrene in the presence of the block copolymer and impregnation with the blowing agent.