In recent years, water jet cutting technology has been being used more and more often, in various domains of human activity. Its numerous applications include cutting different materials - among them, rock materials. The present paper discusses the results of the research that aimed at determining - in a quantitative manner - the way in which the water jet cutting parameters (such as the traverse speed of the head, and the distance between the high-pressure inlet of the water jet and the cut material) influence the quality of the processed surface. Additionally, the impact of these parameters on the surface of various materials was investigated. The materials used were three granites differing with respect to the size of grains. In the course of the research, the standard parameters defined by the ISO norms were analyzed. It was also proposed that variograms be used to analyze the quality of the cut surface.