Vital organs maintain dense microvasculature to sustain the proper function of their cells. For tissue- engineered organs to function properly, artificial capillary networks must be developed. We have microfabricated capillary networks with a biodegradable and biocompatible elastomer, poly(glycerol sebacate) (PGS). We etched capillary patterns onto silicon wafers by standard micro-electromechanical systems (MEMS) techniques. The resultant silicon wafers served as micromolds for the devices. We bond the patterned PGS film with a flat film to create capillary networks that were perfused with a syringe pump at a physiological flow rate. The devices were endothelialized under flow conditions, and part of the lumens reached confluence within 14 days of culture. This approach may lead to tissue-engineered microvasculature that is critical in vital organs engineering.