Tube inversion is a cold forming method which consists of pressing a tube into a radiussed die, which forces the tube edge to inverse producing a second wall. Widely adopted as an energy-absorber process in the automotive industry, it also allows the manufacture of double-walled tubes out of commercial circular tubes and can lead to different products, such as heat exchangers, driving elements and other components. In particular, there are some restrictions in the geometries achievable by the conventional inversion processes: first, the sheet edge is always turned toward the cavity of the double-walled tube; second, the new wall sets at a distance from the first which is strictly related to the diameter-thickness ratio of the initial tube; third, for the outside-in operation the thickness of the second wall grows up to a considerable extent. This paper examines the possibilities of overcoming these restrictions for a double-walled tube. In fact, during the first curling stage of an outside-in tube inversion, it is possible to stop the curling and give a counter curvature to the edge, which will be turned, at the end of the process, outside the cavity. The proper inversion can be then carried out by means of a punch that drives the inversion applying tension at the internal edge rather than applying compression at the external one. This leads to lower loads in the inversion, higher degrees of freedom in the second wall position, a second wall nearly constant thickness and higher accuracies on the product. This particular inversion process enables the creation of easy couplings with other components and also, as an example, to constitute seats of bearings at the extremities of a tube by simple plastic deformation rather than by welding special parts from other technological processes. To perform the tension driven tube inversion, the hole expansion force must be greater than tube inversion force. The forming condition has been developed in terms of geometrical parameters and material properties; experimental confirmation of the results for steel tubes is also given.