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The paper deals with experimental investigations of the influence of laser beam and plasma arc cutting parameters on edge quality of a range of steel grades and thicknesses. Based on the experimental results, a variety of methods have been taken to carry out the analysis of influence of laser beam and plasma arc cutting parameters on the quality and mechanical properties of cut edges of selected high-strength low-alloy (HSLA) strips and plates. In this study, three approaches were investigated corresponding to rank correlation analysis, multidimensional data analysis and decision trees. These techniques were able to elucidate the most relevant cutting parameters as well as the optimal field of values of these parameters to give the required geometrical and mechanical quality levels. As a result of this study, general rules in the form of cutting procedure specifications were established. This was needed to describe the relation between laser beam or plasma arc cutting parameters and the geometrical and mechanical quality factors of cut edges of different medium-and high-strength steel materials. The proposed rules can be also adopted for providing a comparison between the surface qualities achievable by the different combinations of cutting parameters for laser beam and plasma arc cutting processes of medium-and high-strength steels.