A novel method for fabrication of branched, tubular, perfusable microvessels for use in vascular tissue engineering is reported. A tubular, elastomeric, biodegradable scaffold is first fabricated via a new, double fusible injection molding technique that uses a ternary alloy with a low melting temperature, Field's metal, and paraffin as sacrificial components. A cylindrical core metal of 500 μm or lower diameter with the target branching scaffold geometry is first constructed, then the metal structure is coated with paraffin and, finally, the metal-paraffin construct is embedded in polydimethylsiloxane (PDMS). The paraffin layer is then removed by heating and replaced by a biodegradable elastomeric pre-polymer that is subsequently UV-cured inside the PDMS. Next, the metal core is melted away and the PDMS is removed to attain the branched tubular elastomeric biodegradable scaffold. Finally, it is also demonstrated that human umbilical vein endothelial cells (HUVEC) were able to spread on the surface of the scaffold and form a confluent monolayer, confirming the potential of this new technique for making engineered blood vessels.