Blood and lymphatic vessels in the body are central to molecular and cellular transport, tissue repair, and pathophysiology. Several approaches have been employed for engineering microfabricated blood and lymphatic vessels in vitro, yet traditionally these approaches require specialized equipment, facilities, and research training beyond the capabilities of many biomedical laboratories. Here we present xurography as an inexpensive, accessible, and versatile rapid prototyping technique for engineering cylindrical and lumenized microvessels. Using a benchtop xurographer, or a cutting plotter, we fabricated modular multi-layer poly(dimethylsiloxane) (PDMS)-based microphysiological systems (MPS) that house endothelial-lined microvessels approximately 260 μm in diameter embedded within a user-defined 3-D extracellular matrix (ECM). We validated the vascularized MPS (or vessel-on-a-chip) by quantifying changes in blood vessel permeability due to the pro-angiogenic chemokine CXCL12. Moreover, we demonstrated the reconfigurable versatility of this approach by engineering a total of four distinct vessel-ECM arrangements, which were obtained by only minor adjustments to a few steps of the fabrication process. Several of these arrangements, such as ones that incorporate close-ended vessel structures and spatially distinct ECM compartments along the same microvessel, have not been widely achieved with other microfabrication strategies. Therefore, we anticipate that our low-cost and easy-to-implement fabrication approach will facilitate broader adoption of MPS with customizable vascular architectures and ECM components while reducing the turnaround time required for iterative designs.