A 2-D mathematical model is developed in order to simulate a parametric electromagnetic instability oscillation process of a liquid metal droplet under the action of low frequency magnetic field. The Arbitrary Lagrangian-Eulerian （ALE） method and weak form constraint boundary condition are introduced in this model for implementation of the surface tension and electromagnetic force on liquid droplet free surface. The results of the numerical calculations indicate the appearance of various regimes of oscillation. It is found that according to the magnetic field frequency various types of oscillation modes may be found. The oscillation is originated from an instability phenomenon. The stability diagram of liquid metal droplet in the parameter space of magnetic frequency and magnetic flux density is determined numerically. The diagram is very similar to that found in the so-called parametric instability.
