The present inventions in various aspects provide elastic biodegradable polymers. In various embodiments, the polymers are formed by the reaction of a multifunctional alcohol or ether and a difunctional or higher order acid to form a pre-polymer, which is cross-linked to form the elastic biodegradable polymer. In preferred embodiments, the cross-linking is performed by functionalization of one or more OR groups on the pre-polymer backbone with vinyl, followed by photopolymerization to form the elastic biodegradable polymer composition or material. Preferably, acrylate is used to add one or more vinyls to the backbone of the pre-polymer to form an acrylated pre-polymer. In various embodiments, acrylated pre-polymers are co-polymerized with one or more acrylated co-polymers.