Resorbable and elastomeric poly(trimethylene carbonate) (PTMC) networks were efficiently prepared by photoinitiated crosslinking of linear high-molecular-weight PTMC. To crosslink PTMC films, low-molecular-weight PTMC macromers with methacrylate end groups were synthesized and used as crosslinking aids. By exposing PTMC films containing only photoinitiator (Irgacure® 2959) or both photoinitiator and PTMC macromers to ultraviolet light, PTMC networks with high gel contents (87–95%) could be obtained. The crosslink density could be readily varied by adjusting the irradiation time or the amount of crosslinking aid used. The formed networks were flexible, with low elastic modulus values ranging from 7.1 to 7.5 MPa, and also showed excellent resistance to creep in cyclic tests. In vitro experiments showed that the photocrosslinked PTMC networks could be eroded by macrophages, and upon incubation in aqueous cholesterol esterase enzyme- or potassium dioxide solutions. The rate of surface erosion of photocrosslinked PTMC networks was significantly lower than that observed for films prepared from linear PTMC. These resorbable PTMC elastomeric networks are compatible with cells and may find application in tissue engineering and controlled release.