The influence of the main parameters of a dual-mass oscillation system on its dynamic characteristics is examined.   The object of the study comprises the oscillation system of a vibration machine, containing two masses, connected by elastic and dissipative elements. A reduction in the instability of the operating mode when changing the load or frequency of the driving force can be achieved by expanding the resonance zone. Mathematical modelling and simulation experiment approaches were used for the research. Based on the results obtained using the mathematical model for dual-mass oscillation system by Matlab-Simulink, an algorithm is proposed that includes a procedure for forming an amplitude-frequency response with an extended resonance zone and describing the influence of the main parameters of the oscillation system on the location and width of the specified resonance zone. It is shown that with an increase in the second mass of the oscillation system, the horizontal section of the amplitude-frequency response declines and shifts to the region of lower frequencies. This is explained by the increasing inertness of the system to the driving force. With a larger initial mass, the gain of amplitude-frequency response was shown to increase, while the width of the horizontal section decreases. Further, with increased stiffness of the first elastic element, the resonance section descends even lower and shifts towards higher frequency values of the driving force; however, the width of the section increases. Therefore, the method of correcting the amplitude-frequency response by introducing additional mass into the structure of an oscillation machine in order to expand its resonance zone with no additional automated devices seems promising. The obtained results may form the basis for a calculation method for energy-efficient resonance oscillation machines.