The relevance of the research is caused by the need to develop highly-efficient resource-saving equipment, used for kibbling and grinding ore in mining industry. One of the possible solution is the development of ball mills of a vibrating type with AC tractive electromagnet. Connecting a tractive electromagnet to AC voltage source enables a long-range adjustment of operational mode of a ball mill and ensures its operation in quasi-resonant regimes. Mathematical simulation of operational modes of a ball mill of a vibrating type allows determining standards for a vibratory system when changing frequency and value of power supply and generating guidelines to be considered in production prototypes design. Additionally, operation of a ball mill of a vibrating type in quasi-resonant regimes is followed by significant reduction of energy consumption along with productivity gain. The aim of the research is to develop a mathematical model of operation of a ball mill of a vibrating type with a tractive electromagnet powered by a variable frequency power supply; in terms of the developed mathematical model to calculate the operational modes of a ball mill of a vibrating type and generate the guidelines for use in developing a ball mill. Methods. Mathematical simulation of operational modes of a ball mill was carried out by a numerical solution of a differential system of elements movement in a vibratory system. Vibratory system parameters were calculated with regard to objective technical data of the similar equipment produced. Results. The mathematical model of a ball mill of a vibrating type allows determining a range of effective tractive efforts and power supply frequencies of a tractive electromagnet, relevant to a quasi-resonant operation mode when changing vibratory system parameters. With the appropriate quasi-resonant frequency span and masses of elements of a vibratory system we can determine tractive electromagnet parameters, design and specification of a spring suspension of a ball mill.