Synthetic vascular grafts are useful to bypass diseased arteries. The long-term failure of synthetic grafts is primarily due to intimal hyperplasia at the anastomotic sites. The accelerated intimal hyperplasia may stem from a compliance mismatch between the host artery and the graft since commercially available synthetic conduits are much stiffer than an artery. The objective of this thesis is to design a method for fabricating a vascular graft that mechanically matches the patients native artery over the expected physiologic range of pressures. The creation of an optimized mechanical graft will hopefully lead to an improvement in patency rates. The mechanical equivalency between the graft and the host artery is defined locally by several criteria including the diameter upon inflation, the elasticity at mean pressure, and axial force. A single parameter mathematical for a thin-walled tube is used to describe of the final mechanical behavior of a synthetic graft. For the general problem, the objective would be to fabricate a mechanics-matching vascular graft for each host artery. Typically, fabrication parameters are set initially and the properties of the fabricated graft are measured. However, by modeling the entire fabrication process and final mechanical properties, it is possible to invert the situation and let the typical output mechanical values be used to define the fabrication parameters. The resultant fabricated graft will then be mechanically matching. As a proof-of-concept, several prototype synthetic grafts were manufactured and characterized by a single Invariant to match a canine artery. The resultant graft equaled the diameter upon inflation, the elasticity at mean pressure, and axial force of the native canine artery within 6%. An alternative to making an individual graft for each artery is also presented. A surgeon may choose the best graft from a set of pre-manufactured grafts, using a computer program algorithm for best fit using two parameters in a neighborhood. The design optimization problem was solved for both canine carotid and human coronary arteries. In conclusion, the overall process of design, fabrication and selection of a mechanics matching synthetic vascular graft is shown to be reliable and robust.