<p>This research is focused on the calculation of a reasonable detonator delay time for realizing cut blast vibration control. First, the viscoelastic rock mass parameters corresponding to the engineering rock mass quality classification were determined based on wave theory of Kelvin medium. Then, a calculation model was obtained for the millisecond-delay cut blast vibration in Kelvin media using the Starfield charge superposition principle. Further, the influence of the delay time on the cut blast vibration was quantitatively analyzed and a method for calculating the reasonable cut blasting millisecond delay time is proposed according to the principle of dimensional analysis. Finally, field tests were used to verify the applicability of the method. The results show that 5 ms to 20 ms is a better detonator delay time range and cut blasting vibration can be effectively controlled using the delay time calculated by the calculation model described in this paper.</p>