External reinforcement has been suggested for autologous vein grafts to address the mismatch of mechanical properties and fluid dynamics of graft and host vessel, a main factor for graft failure. A finite-element tool was developed to investigate the mechanical behaviour, in particular radial compliance, of knitted Nitinol meshes (internal diameter: 3.34 mm) with two different knit designs (even versus uneven circumferential loops) and three different wire thicknesses (0.05, 0.0635 and 0.075 mm) under physiological conditions. The Nitinol material parameters were obtained from experimental testing. The compliance predicted for the 80-120 mmHg physiological blood pressure range was 2.5, 0.9 and 0.6%/100 mmHg for the even loop design and 1.2, 0.5 and 0.5%/100 mmHg for the uneven loop design, for wire thicknesses of 0.05, 0.0635 and 0.075 mm. The highest stress, at 120 mmHg, was found in the even loop mesh with the thinnest wire to be 268 MPa, remaining 44.5% below the stress initiating stress-induced phase transformation. The maximum stress decreased to 132 and 91 MPa with increasing wire thickness of the same loop design. The uneven loop design exhibited maximum stress levels of 65.3%, 63.6% and 87.9% of the even loop values at 0.05, 0.0635 and 0.075 mm wire thickness. The maximum strain of 0.7%, at 120 mmHg, remained un-critical considering a typical high-cycle recoverable strain of 2%. It was demonstrated that the numerical approach developed was feasible of effectively evaluating design variations of knitted Nitinol meshes towards vein graft behaviour equivalent to arterial mechanics.