As the incidence of cardiovascular diseases has been growing in recent years, the need for small-diameter vascular grafts is increasing. Considering the limited success of synthetic grafts, vascular tissue engineering/repair/regeneration aim to find novel solutions. Silk fibroin (SF) has been widely investigated for the development of vascular grafts, due to its good biocompatibility, tailorable biodegradability, excellent mechanical properties, and minimal inflammatory reactions. In this study, a new generation of three-layered SF vascular scaffolds has been produced and optimized. Four designs of the SILKGraft vascular prosthesis have been developed with the aim of improving kink resistance and mechanical strength, without compromising the compliance with native vessels and the proven biocompatibility. A more compact arrangement of the textile layer allowed for the increase in the mechanical properties along the longitudinal and circumferential directions and the improvement of the compliance value, which approached that reported for the saphenous and umbilical veins. The higher braid density slightly affected the grafts’ morphology, increasing surface roughness, but the novel design mimicked the corrugation approach used for synthetic grafts, causing significant improvements in kink resistance.