Biodegradable elastomeric networks were prepared from ethyl fumarate-functionalized poly(trimethylene carbonate) oligomers. Photocrosslinkable macromers were synthesized by reacting three-armed, hydroxyl group-terminated poly(trimethylene carbonate) oligomers with fumaric acid monoethyl ester at room temperature using N,N-dicyclohexylcarbodiimide as a coupling agent and 4-dimethylamino pyridine as a catalyst. Poly(trimethylene carbonate) macromers with molecular weights ranging between 4500 and 13,900 were prepared and crosslinked by ultraviolet-initiated radical polymerization. The gel contents of the resulting transparent networks varied between 74% and 80%. All obtained networks had low glass transition temperatures, which varied between −18 and −13 °C. They showed rubber-like behavior and excellent mechanical properties, with tensile strengths and elongations at break of up to 17.5 MPa and 750%, respectively. Moreover, static- and dynamic creep experiments showed that these amorphous networks were highly elastic and resistant to creep. In cyclic tensile testing to 50% strain, the permanent deformation after 20 cycles was 0%, while static creep tests at 35% of the yield stress did not indicate creep or permanent deformation after removal of the load. Porous structures were prepared by photopolymerizing the macromers in the presence of salt particles, and subsequent leaching of the salt. Such networks, built up of non-toxic compounds and designed to release benign degradation products, may find application as tissue engineering scaffolds for dynamic cell culture.