Tube bending is used in different industries such as aerospace, furniture, home apliances, decorations, traortation, petrochemical industries etc, and new applications can be continuously found every day, therefore various methods of bending are invented. Tube bending commonly has two different catagories: cold bending and hot bending. Each category can be divided into several subdivisions. In this research various cold bending methods will be explained first. Then free bending which is one of the most recent and one of the cold tube bending methods will be explained in more detail. This method is especially suitable for bending thin wall tubes and has many applications in different industries. Free bending is capable to produce 2D and 3D bends and has a limitation of bend radius to tube diameter of 2.5(R/D=2.5). CNC free bendig machine is a high cost machine and its bending dies need high tolerances. In Iran there are a few companies which use free bending method. Since the method is new, there are relatively few published research about Free Bendig CNC Machines and process. In this thesis, different cold tube bending methods and their limitations are explained first, then free bending mehod and free bendig CNC machine will be explained in more details. Free bending CNC machine uses one fixed die and one movable die. Fix die and movable die are connected to each other with a spherical joint. By displacing movable die while tube is fed through the dies, tube is bent. Movable die can just move in one plane parallel to the fixed die surface with a constant distance apart. Movable die is tangent to the tube in all instances. After introducing free bending method and its history, other researchers’ activities about free bendig method and free bending CNC machine will be mentioned. Then, formulation fundamentals of free bending CNC machine and procedure of construction desired 3D bendings are explained. This procedure of producing desired 3D bends is checked incrementally. For incremental validation of the proposed technique, different points of a desired curve are obtained by using a CAD software. Then curve fitting will be performed through the selected points, by Matlab and the parametric equation of the curve will be obtained. Tangent vector of the curve will define direction and location of the movable die with respect to the fixed die at each point. Due to springback effects and material tolerances some offset should be taken into account to modify theoretical predictions. Then simulation of free bendig process will be performed by Abaqus software. Abaqus levels are explained, step by step and the result will be checked with experiments and other available published international papers. There are some sorces of error due to geometrical tolerances of die and tube and also friction effects. These factors can greatly affect repeatability of the process. It was concluded that for a repeatable bending process close geometrical tolerances should be observed during die manufacture as well as tube diameter selection. It is shown that the proposed incremental procedure, to obtain a desired 3D curve, is valid and matches with experiments. Keywords: Tube bending, CNC free bending, 3D curve and bends, fixed die, moveable die, abaqus