The process of the abrasive water jet cutting of materials, supported by the theories of fluid mechanics, abrasive wear and damage mechanics, is a high-tech technologies that provides unique capabilities compared to conventional machining processes. This paper, along the theoretical derivations, provides original contributions in the form of mathematical models of the quantity of the cut surface damage, expressed by the values of cut surface roughness. The particular part of this paper deal with the results of the original experimental research. The research aim was connected with the demands of industry, i.e. the end user. Having in mind that the conventional machining processes are not only lagging behind in terms of quality of cut, or even some requests are not able to meet, but with the advent of composite materials were not able to machine them, because they occurred unacceptable damage (mechanical damage or delamination, fiber pull-out, burning, frayed edges).