Recent interest in reducing dependency on oil and transitioning to renewable sources has increased the research in biofeedstock as replacements of oil based products. Our research involves two different methods of producing elastomeric block copolymers using Acrylated Epoxidized Soy Bean Oil (AESO), a renewable biofeedstock as a substitute of the elastic component in modern elastic materials. Butadiene when polymerized forms long linear chains that makes it suitable to be used as an elastic material and is commonly used as the rubbery component in many applications. Acrylated epoxidized soybean oil and styrene were polymerized by two different polymerization techniques, Atom Transfer Radical Polymerization (ATRP) and Reversible Addition Fragmentation Chain Transfer (RAFT) Polymerization. Each technique was able to individually create diblock and triblock copolymers, resulting in polymers that are predominantly non-crosslinked linear or with lightly branched chains. These materials behave as elastomers/rubbers at room temperature but reversibly melt and are susceptible to common processing techniques at elevated temperatures and making them suitable for a broad number of applications, ranging from adhesives to asphalt modifiers.