Dynamically partially cured composition comprising a peroxide-curable olefin copolymer rubber (such as EDPM) and a peroxide-decomposing olefin plastic (such as PE and PP) is improved by effecting the dynamic heat-treatment with addition of a peroxide-non-curable hydrocarbon rubber (such as PIB) and/or a mineral oil softener (process oil). The dynamic heat-treatment is preferably carried out not only in the presence of an organic peroxide but also in the presence of divinyl benzene. The elastomeric composition is thermoplastic and, with or without further blending with an olefin plastic, is processable by techniques conventionally used for thermoplastic resins. This elastomer composition and blends of the elastomer composition and olefin plastic can be used for producing foamed product in combination with decomposition type foaming agent (such as azodicarbonamide).