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In this paper, the modified couple stress theory is used to investigate the effects of mechanical shocks due to package motions on the dynamic stability of a fully clamped rectangular micro-plate. Numerical results reveal that the intrinsic size dependence of materials on thickness affects the stability region, and the dynamic response of the micro-plate. The results obtained from the modified couple stress theory show that the classical theory overestimates the deflection of the micro-plate in smaller thicknesses, which may lead to early instability. In contrast, the results of the modified couple stress theory are similar to those of the classical elasticity theory in greater thicknesses. Therefore, the effect of intrinsic length-scale can be neglected in this case. In addition, studying a half-sine mechanical shock shows that changing the pulse duration can cause the dynamic shock response to become similar to the quasistatic one while changing the amplitude of the acceleration pulse can change the stable voltage values of the micro-plate. These parameters should be considered together with the pullin voltage to prevent the failure of MEMS devices under mechanical shocks.