A significant drawback of the rigid synthetic vascular prostheses used in the clinic is the mechanical mismatch between the implant and the prosthetic vessel. When placing prostheses with radial elasticity, in which this deficiency is compensated, the integration of the graft occurs more favorably, so that signs of cell differentiation appear in the prosthesis capsule, which contributes to the restoration of vascular tone and the possibility of vasomotor reactions. Aortic prostheses fabricated by electrospinning from a blend of copolymers of vinylidene fluoride with hexafluoropropylene (VDF/HFP) had a biomechanical behavior comparable to the native aorta. In the present study, to ensure mechanical stability in the conditions of a living organism, the fabricated blood vessel prostheses (BVP) were cross-linked with γ-radiation. An optimal absorbed dose of 0.3 MGy was determined. The obtained samples were implanted into the infrarenal aorta of laboratory animals—Landrace pigs. Histological studies have shown that the connective capsule that forms around the prosthesis has signs of high tissue organization. This is evidenced by the cells of the fibroblast series located in layers oriented along and across the prosthesis, similar to the orientation of cells in a biological arterial vessel.