The current problems associated with the maintenance of hard coal longwall mining dependon the application or use of extraction technologies. In order to make the best use of these technologies,a new approach based on simulation studies is necessary. This paper aims to develop a mathematicalmodel for the powered roof support’s operation. The three groups of professionals involved inthe testing of the roof support were involved in the work on changing the hydraulic system of thepowered roof support stand. These professionals were powered roof support’s designers, researchersand users. The research subject was the development of a mathematical model as a starting pointfor conducting simulations. The model is based on d’Alembert’s principle and the equation of thebalance of flow rates. Based on the developed model, it is possible to determine the pressure inthe space under the piston of the hydraulic prop. The results obtained in the simulations are thebasic assumptions for the development of a prototype that would solve the current problems inthe hydraulic systems of powered roof supports. The adopted research methodology assumed thedevelopment of a mathematical model, simulation in the MATLAB environment and verificationof the model on a test stand. The obtained results of simulation tests based on the developedmathematical model were confirmed in bench tests. Simulation and bench tests determined thecorrectness of the assumptions made for the development of the prototype model. Based on theanalysis of the results, the nature of the work of the future prototype has been predetermined. Thenext stage will be the testing of the prototype, which is to be included in the hydraulic system of theprop of powered roof support in the future. The model mentioned before is the baseline model, andit will be modified depending on the application of the future design in real conditions. Simulationstudies of powered roof support will allow the structure that is used currently to be optimised, so asto adapt it to increasingly difficult working conditions.