A vertical rod with a free upper end and with a clumped or a simply supported lower end is considered. The support is subjected to harmonic vibrations. The aim is to find the level of vibrations such that the vertical position of rod is stable. Both bending and longitudinal vibrations are taken into account. To describe the bending vibrations the model of Bernoulli-Euler beam is applied. In order to determine the critical value of the vibration the two-scaled asymptotic expansions are used.