For success in vascular surgery involving small-diameter ( 6 mm) vessels, a graft must closely match the internal diameter of the host artery and have desired high elasticity, porosity and transverse compliance. Thus although arterial grafts have gained acceptance in larger-calibre ( 6 mm) applications, where the requirements are flexible, a vein from the body continues to be preferred for small-vessel repair. The objective of this study is to develop an understanding of the material and the construction factors that affect the values of a woven tube's diameter, pore size, elastic recovery and transverse compliance. This information is largely absent in literature. By varying yarn size and fabric structure, seamless tubes (1.5-7 mm diameter) were constructed. These were heat set for circular shapes and characterised for size, geometry and radial elasticity. Property-structure correlation models are presented. Grafts of desired size can be engineered and their properties predicted.