Designed flexible and elastic network structures are prepared by stereolithography using a photo-crosslinkable resin based on a poly(trimethylene carbonate) (PTMC) macromer with a molecular weight of 3150 g/mol. Physical properties and the compatibility with human umbilical vein endothelial cells (HUVECs) are evaluated. The hydrophobic networks are found to be flexible and elastic, with an E modulus of 7.9 ± 0.1 MPa, a tensile strength of 3.5 ± 0.1 MPa and an elongation at break of 76.7 ± 0.7%. HUVECs attach and proliferate well on the surfaces of the built structures. A three-dimensional microvascular network is designed to serve as a perfusable scaffold for tissue engineering. In the design, 5 generations of open channels each branch into 4 smaller channels yielding a microvascular region with a high density of capillaries. The overall cross-sectional area through which medium or blood can be perfused remains constant. These structures would ensure efficient nourishment of cells in a large volume of tissue. Built by stereolithography using the PTMC resin, the smallest channels of these structures have square cross-sectional areas, with inner widths of approximately 224 μm and wall thicknesses of approximately 152 μm. The channels are open, allowing water to perfuse the scaffold at 0.279 ± 0.006 mL/s at 80 mmHg and 0.335 ± 0.009 mL/s at 120 mmHg.