To select a rational method for cutting of rolled stocks made from materials with different physical and mathematical properties, an engineer must have the tools to make such a choice. For this, it is proposed to use the well-known synergistic material fracture criteria. In order to find the most informative system of synergetic criteria allowing to classify materials authentically by their fracture sensitivity, the software was developed. It allows to solve the clustering problem in a multidimensional space of parameters and present the obtained information in a visual form using self-organizing Kohonen maps. The cluster analysis of the synergetic criteria of fracture material was carried out. The most informative criterion among the ones characterizing the mechanical properties of steels is the «offset yield strength», among the synergistic ones – «scale criterion». At the same time, among the traditional mechanical features of steels, a set allowing to classify materials with a given integrity by their cutting sensitivity has not been found. It was established that the synergistic criteria: «crack propagation criterion» and «brittleness criterion» are basic informative features. When adding any of the remaining complex criteria («crack nucleation criterion» or «scale criterion»), they form the most informative sets of minimal power, providing the classification of materials by their cutting sensitivity with a given integrity. In order to obtain high quality billets at a minimum conversion cost, recommendations were developed for choice of the method for cutting of rolled stocks in magnitude of criteria values: «crack propagation criterion» and «brittleness criterion». To cut materials «in plastic state», the cutting with a shear should be used, specifically – a closed cut-off scheme or an incompletely closed cut-off scheme with an active transverse clamp or a cut-off scheme with a differentiated rolling clamp. If increased requirements are imposed on the geometric accuracy of the billets, it is recommended to use complex blanking and cutting processes. For cutting materials «in elastoplastic state» there are good reasons to use a cut with a shear, and in particular – an incompletely closed cut-off scheme with an active and passive transverse clamp. Closer to the class interval, it is possible to apply cold bend breaking with the application of an effective stress concentrator. Cold bend breaking should be used to cut «brittle» materials. The carried out experiments confirmed the adequacy of theoretical conclusions and recommendations on the choice of a rational method for cutting of the rolled stocks to obtain high quality billets.