The present invention provides a radiation-curable prepolymer. The radiation-curable prepolymer of the invention is prepared by reacting an isocyanate-capped polyurethane with an ethylenically unsaturated amine or an ethylenically unsaturated monohydroxy compound or a mixture thereof, wherein the isocyanate-capped polyurethane is a copolymerization production of: (a) at least one polyalkylene glycol; (b) at least one branching agent having at least three hydroxy groups; and (c) at least one di- or polyisocyanate. The radiation-curable prepolymer of the invention can find use in economically producing contact lenses which have durable, highly elastic soft contact lenses with desired physical properties. In addition, the present invention provides method for making a radiation-curable prepolymer of the invention and for making a medical device, preferably an ophthalmic device, more preferably a contact lens.