Plasma jet cutting is a nonconventional thermoelectric process widely used in metal processing and shipbuilding industry. Plasma jet is generated by dissociation and ionization of plasma gas and it is capable of cutting different types of metals with wide range of thicknesses. As a material, aluminium is known for its relatively low density, high thermo and electrical conductivity with significant corrosion resistance. Therefore, it has been particularly used in shipbuilding industry, as well as in designing various types of constructions. Due to their properties, plasma jet cutting of aluminium alloys raises a certain dose of insecurity regarding process factors value definition, as well as achieving optimal cut quality. In this paper, a research of plasma jet cutting suitability of aluminium alloy AlMg4.5Mn (EN AW 5083) was conducted. Experimental work was carried out on three different sheet thicknesses. For each sheet thickness, in the frame of experimental hyperspace, constraints i.e. process factors combinations which do not lead to cuts were identified. Using different modeling methods: artificial neural networks, fuzzy logic and regression, influence of variable cutting process factors on output cut quality characteristics was described. Moreover, preconditions for creating expert system which could be supplemented with additional experimental results were realized.. Using different optimization methods: Taguchi method, desirability analysis and metaheuristic optimization by genetic algorithm, one objective and multiobjective optimization were conducted. Achieving of maximal possible cut quality as well as productivity, was considered also through the use of these methods in order to determine optimal cutting area. Obtained results represent good foundation for control and further improvement of cutting process