The invention claimed concerns a medical material for reconstruction of blood vessels, the method of its production, as well as the application of that medical material reconstruction of blood vessels. More precisely, the invention concerns textile vascular prostheses for the reconstruction of small diameter blood vessels and solvent-free manufacturing method used to obtain the aforementioned small diameter vascular prostheses. The solution presented in this patent application concerns a new method of forming textile nanostructures to be applied in vascular surgery and cardiosurgery, especially in prosthetics of blood vessels below 6 mm in diameter, as well as a substrate for proliferation of vascular endothelium cells.