A process for preparing modified diene polymer rubbers having an increased impact resilience and a reduced hardness at low temperatures and useful as rubber materials for automobile tires and other industries which comprises producing an alkali metal-containing conjugated diene polymer, and reacting the alkali metal-containing polymer with a modifier selected from the group consisting of an acrylamide compound of the formula:
wherein R¹ is hydrogen atom or methyl group, R² and R³ are independently an alkyl group and n is an integer, and an aminovinylsilane compound of the formula:
wherein R⁴ to R⁸ are independently an alkyl group, said alkali metal-containing diene polymer being prepared by a living anionic polymerization using an alkali metal-based catalyst or by an addition reaction of a diene polymer having conjugated diene units and an alkali metal-based catalyst in a hydrocarbon solvent. The modified diene polymers can be incorporated with usual rubber additives and with or without other rubbers to provide rubber compositions for various purposes, and the cured products show an increased impact resilience and a reduced hardness at low temperatures.