The paper reports the results of research aimed at creating theoretical grounds for a new method of mandrelless small-radius tube bending (1.5Dr<Rg<2.5Dr, where Dr - tube diameter, Rg - bending radius). As the result of applying such a methodology it is possible to carry out the bending process (with an angle of up to 180°) and obtain an ovalization and wall thinning in the bending area, which are much smaller than those in currently manufactured products. The currently used bending methods and bending equipment are able to achieve a minimum bending radius not less than three times the tube outer diameter. The research hypothesis has assumed the existence of tube bending methods that are more efficient that those known so far. Than methods do not rely on circular bending contours, but instead they may use other shaping die contours which has not been explored yet. Circular benders used in practice fail in that they do not yield the expected results on small radii and do not control the material flow (do not ensure its correct behaviour) in the bending zone. The literature review has shown that there are currently no theoretical studies, numerical analyses and experimental verifications related to the processes of mandrelless tube bending on small radii, i.e. for 1.5D≤R≥2.5D, where: (R - bending radius, D - tube outer diameter) up to an angle of 180°. Due to the lack of studies on this subject, in their approach to the numerical modelling of the problem, the authors of the paper were guided by their own experience in this field and made every effort to make the numerical model reflect the actual process as accurately as possible. They were only aided by the general knowledge accumulated in the literature on numerical modelling. To sum up, the purpose of the publication is to demonstrate that the change in the die recess towards a shape resembling an ellipse results in a change in the characteristics of metal flow (movement) along the tube perimeter and in a change in the stress characteristics and, as a consequence, a change in the tube cross-section in the bending zone. The research discussed in this paper seeks to establish the correct flow of material in the tube cross-section in the bending zone by determining the most efficient bender recess shape and friction surface forming, which will eliminate the excessive ovalization and upper wall thinning. The expected effect of implementing this bending technology will be increasing the flow capacity in energy systems, which will directly translate into a reduction of atmospheric CO emissions due to the lower energy consumption. In addition, the paper has presented the concepts of tools intended for the experimental verification of tube bending process.