Autologous or synthetic vascular grafts are used routinely for providing access in hemodialysis or for arterial bypass in patients with cardiovascular disease. However, some patients either lack suitable autologous tissue or cannot receive synthetic grafts. Such patients could benefit from a vascular graft produced by tissue engineering. Here, we engineer vascular grafts using human allogeneic or canine smooth muscle cells grown on a tubular polyglycolic acid scaffold. Cellular material was removed with detergents to render the grafts nonimmunogenic. Mechanical properties of the human vascular grafts were similar to native human blood vessels, and the grafts could withstand long-term storage at 4 °C. Human engineered grafts were tested in a baboon model of arteriovenous access for hemodialysis. Canine grafts were tested in a dog model of peripheral and coronary artery bypass. Grafts demonstrated excellent patency and resisted dilatation, calcification, and intimal hyperplasia. Such tissue-engineered vascular grafts may provide a readily available option for patients without suitable autologous tissue or for those who are not candidates for synthetic grafts.