Rubbery biodegradable cross‐linked poly (1,3‐trimethylene carbonate) (PTMC) networks were prepared by gamma irradiation under vacuum in the presence of trimethylolpropane triacrylate (TMPTA), pentaerythritol triacrylate (PETA), and pentaerythritol tetraacrylate (PET4A). The effect of crosslinking agent, crosslinking agent content (1, 3, 5, 7 wt%), and irradiation dose (25, 50, 75, 100, 125 kGy) on PTMC networks were evaluated. The crosslinking efficiency of PETA was better than that of TMPTA and PET4A at a standard sterilization dose of 25 kGy. The PTMC network with gel fractions up to 92% ± 1% and tensile strength up to 26.0 ± 2.2 MPa could be obtained by adding 7 wt% PETA. The increase in irradiation dose reduced the gel content and network density, and led to a decrease in mechanical properties. The PTMC network extracted by ethanol showed better flexibility and mechanical properties. The irradiation crosslinking of PTMC with 7 wt% PETA followed the Chen–Liu–Tang equation instead of the Charlesby–Pinner equation. The incorporation of crosslinking agents improved the creep resistance and thermal stability, resulting in low permanent set values (5.5%). Furthermore, the enzymatic erosion rates of the networks decreased. Therefore, these PTMC networks can be utilized in a broad range of soft tissue engineering.