Changes in dimensional and mechanical properties of degradable sheaths in poly lactic-co glycolic acid (PLGA) have been researched extensively. Composite PLGA having variable resorption rates in multiple layers under physiological loading has not been reported. Our novel design of a PLGA sheath is composed of 3 layers with different degradation rates (i.e., the innermost layer degrades the fastest, followed by the middle, while the outer layer degrades the slowest). In the presence of physiological luminal pressure, diameter is greater, thickness is less, resorption rate is greater, pore size is greater, and incremental modulus is greater than in nonpressurized sheaths. Furthermore, the ratio of the pore size to the sheath radius affects the dimensional changes of the sheath in the radial direction. In addition to changing the pore size-to-sheath radius ratio, the dimensional changes can be manipulated by choosing different glycolic and lactic acid ratios for the different layers. The application of this novel PLGA design for gradual arterialization of vein grafts is contemplated.