Abstract: The principle of driving point anti-resonance vibratory machines is introduced, with the expressions of the upper/lower body's steady amplitude derived. The concepts of the reliability and reliable exciting-frequency range of driving point anti-resonance vibratory machines are proposed. The randomness of vibratory machine parameters caused by manufacturing, installation and other errors is analyzed. Furthermore, the random perturbation method is used to analyze the amplitude response of the vibratory machine to the exciting frequency and to quantize the amplitude stability condition, thereby obtaining the exciting-frequency range in which the vibratory machine can work reliably. This work provides an effective approach to verifying the rationality of parameters selection and choosing the effective exciting-frequency range. Finally, a numerical example is given.