Cold volume deforming is one of the progressive methods of obtaining high-quality products. One of the tasks of cold volume deforming processes is to increase the limiting dimensions of parts and ensure their high and stable mechanical properties. This problem can be solved by introducing new progressive and innovative methods of volume plastic processing. Such methods include combined step-by-step processes of cold volume extrusion. These processes are difficult to implement, but allow to get products of complex configuration with increased limiting dimensions. Since combined processes are characterized by deformation in several stages, there is a problem of assessing the deformability of the workpiece due to multiple changes in the nature of the load. Therefore, in the article, using the example of the extrusion process of a rod with a flange, a sequence of calculations of the used plasticity resource, taking into account the features of the non-monotonic load, was proposed. The main elements of this sequence include the evaluation of the kinematic characteristics of plastic flow using spatial and material reference frames, the assessment of the stress state based on the model of an anisotropically hardening body, and the determination of the value of the used plasticity resource applying a tensor approach of the damage accumulation process, which includes a component of the guiding indicator in the integrand. As a result, the deformability of the workpiece in the combined process of radial extrusion with subsequent upsetting of the flange obtained was estimated. The value of the used plasticity resource at characteristic points of the workpiece volume was determined. For workpieces made of steel 1010 and aluminum alloy AA3003, it has been shown that radial extrusion followed by flange upsetting makes it possible to obtain a flange with a diameter almost 3 times greater than the initial diameter of the workpiece.