Purpose. The present paper studies the dependence of the dynamic oscillatory movements in the area of drill string sticking on the parameters of vibrating mechanism and place of its installation in the heavy weight drill pipe. The authors focus specifically on conditions responsible for resonant vibrations excitation in the drill string, which facilitates the release of stuck drill pipe. The aim is to use the results of the research in the development of the method for vibrator application, to

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... ork out recommendations concerning the choice of its installation place in the heavy weight drill pipe, its tuning to the resonant frequency, the choice of induced force amplitude. Methods. The authors proposed a mathematical model of the drill string functioning with vibration mechanism installed into the heavy weight drill pipe. The vibrator is needed to eliminate sticking of the drilling tool. The suggested discretecontinuum model which takes wave processes into account allows to conduct grounded experimental research. Findings. The developed mathematical model served as the basis for designing a computer program aimed to visualize oscillatory processes taking place in the string of pipes, and to calculate basic dynamic and kinematic characteristics of the analyzed system. Frequency oscillation spectrum was calculated for the selected layout of the drill string and the resonant amplitudes at these frequencies. Originality. The proposed technique allows to significantly determine strains, stresses and safety margins in the arbitrary drill string section more accurately and to predict its sticking while drilling oil and gas boreholes. Practical implications. A specific method of selecting a place for the vibrator installation was elaborated. Recommendations concerning the choice of installation site, amplitude of excitation force, resonant frequencies for elimination of pipes' sticking and prevention of drill strings destruction are provided.