Tubular grafts based on nanofibers of copolymer of epsilon-caprolactam and hexamethylendiaminadipate were obtained by the electrospinning method. The strength of materials based on the dry nanofibers was 6.2 MPa with elongation at break of 133%, or 7.5 MPa and 299% in saline, respectively. The pressure value at which liquid started seeping through the tube wall was P = 10 kPa. Absence of cytotoxicity was proved, as well as adhesion and proliferation of mesenchymal stem cells on the surface. Tubes with inner diameter of 1 mm were tested in vivo in rat abdominal aorta. A layer of endothelial cells was shown to form on the inner side of the prosthesis after 30 days. There was no evidence of stenosis or dilatation of the prosthesis after 14 months with observation of endothelial and subendothelial layers.