This review is devoted to the development of a technique for the fabrication of tubular samples based on needleless electrospinning. Such materials have the potential for use in a wide range of tissue engineering applications including glaucoma drainage devices, vascular grafts, peripheral nerves, and the repair of the urethra. Since needle electrospinning is a time-consuming method, concerning which it is difficult to regulate the ambient conditions, Nanospider technology was employed for the fabrication of the tubular-shaped samples. A special device was constructed and inserted into the electrospinning chamber of the Nanospider machine. The feasibility of the use of the device was proven via electrospinning of polycaprolactone. The testing of the productivity of the needle and the needleless methods proved that needleless technology is four to five times more efficient than the needle electrospinning approach.