The current problems associated with the maintenance of hard coal longwall mining depend on 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 mathematical model for the powered roof support’s operation. The three groups of professionals involved in the testing of the roof support were involved in the work on changing the hydraulic system of the powered roof support stand. These professionals were powered roof support’s designers, researchers and users. The research subject was the development of a mathematical model as a starting point for conducting simulations. The model is based on d’Alembert’s principle and the equation of the balance of flow rates. Based on the developed model, it is possible to determine the pressure in the space under the piston of the hydraulic prop. The results obtained in the simulations are the basic assumptions for the development of a prototype that would solve the current problems in the hydraulic systems of powered roof supports. The adopted research methodology assumed the development of a mathematical model, simulation in the MATLAB environment and verification of the model on a test stand. The obtained results of simulation tests based on the developed mathematical model were confirmed in bench tests. Simulation and bench tests determined the correctness of the assumptions made for the development of the prototype model. Based on the analysis of the results, the nature of the work of the future prototype has been predetermined. The next stage will be the testing of the prototype, which is to be included in the hydraulic system of the prop of powered roof support in the future. The model mentioned before is the baseline model, and it will be modified depending on the application of the future design in real conditions. Simulation studies of powered roof support will allow the structure that is used currently to be optimised, so as to adapt it to increasingly difficult working conditions.