Abstract: The process for producing shock-proof graft copolymers of styrene with synthetic rubber consists in that rubber is dissolved in styrene at a maximum temperature of 75.degree. C. The resultant solution is subjected to prepolymerization by being heated to 75-85.degree. C. in the presence of a plasticizer and a peroxide initiating agent. The peroxide initiator is essentially a composition of the following formulation (in parts by weight): diacylated peroxides of aliphatic acids C.sub.3 -C.sub.5, 2 to 8; diacylated peroxides of aliphatic acids C.sub.6 -C.sub.9, 80 to 89; diacylated peroxides of aliphatic acids C.sub.10 -C.sub.12, 7 to 14. The prepolymerization process proceeds until the 25-40 percent styrene conversion. The result is the prepolymer which is exposed to aqueous-suspension polymerization by being heated in an aqueous medium to maximum 140.degree. C.