This article investigates the relationship of rotation angle of two ends of elastic guidewires, and motion method of guidewires and catheters in bifurcated blood vessels. The relationship of rotation angles of the two ends of the guidewire has first been studied by mathematical reasoning, indicating that the rotation angle of the front end of guidewire can be precisely described by that of the rear end. In order to satisfy the requirements of different vascular interventional surgeries, we further investigated a general model of bifurcated human blood vessels. Based on this model, a new motion method, which ensures the guidewire and catheter move cooperatively along center lines of blood vessels to the final target point, has been introduced. Rotation angles of the guidewire in this model were then analyzed. By experiments to verify the functional relationship between rotation angles of two ends of guidewire, the motion method and algorithm of guidewire and catheter are correct. Our study provides references for future studies in fully automated vascular interventional surgeries.