An arterial graft with a corrugated cylindrical cross-section has been proposed as a partial solution to the problem of elastic stiffness mismatch between conventional grafts and arterial tissue (Trescony et al., 1994, US Patent 5,282, 847 (granted February 1 1994)). A two-dimensional ring theory model and a finite element shell theory model are used to study the inflation under uniform interior pressure of grafts with noncircular cross-sections as a first approximation to their behavior in vivo. For the physically relevant range of area expansions (typically 7-10%) and pressures (8-18 kPa), corrugations can significantly reduce the graft stiffness in comparison to conventional circular cross-section grafts.