Drives with electromagnetic vibration exciters (EMVE) occupy an important place among the vibration machines used in various industries owing to their having a simple design and ensuring high vibration intensity. Rational designing of such devices needs a theoretical justification. An electromagnetic vibrator was theoretically studied, as a result of which regularities interrelating its electrical, magnetic and mechanical subsystems have been established, and the dependence of coil inductance on the gap x that takes into account the inductance modulation coefficient has been determined. Correlations describing periodic solutions in the form of series in powers of a small parameter µ have been derived. Equations using which the stability of periodic solutions can be determined in a first approximation have been obtained. By using the small parameter method, relations for the current in the coil have been derived, and the power consumed by the electromagnet has been determined.