The behaviour of drops in an acoustic levitator is simulated numerically. The ultrasound field is directed along the axis of gravity, the motion of the drop is supposed to be axisymmetric. The flow inside the drop is assumed inviscid (since the time intervals considered are short) and incompressible. First, as a test case, we consider a stationary ultrasound wave. We observe, as in previous experimental and theoretical works, that stable drop equilibrium shapes exist for acoustic Bond numbers up to a critical value. The critical value depends on the dimensionless wave number of the ultrasound. Beyond the critical value, we still observe equilibrium drop shapes, but they are not purely convex (i.e. "dog-bone" shaped) and found to be unstable. Next we modulate the ultrasound pressure level (SPL) with a frequency omega(2), which is comparable to the first few drop resonance frequencies, and a small modulation amplitude. Simulations and experiments are performed and compared-, the agreement is very good. We further on investigate numerically the more general case of an arbitrary omega(2) (still comparable to the first few drop resonance frequencies, yet). A very rich drop dynamics is obtained. We observe that a resonant drop break-up can be triggered by an appropriate choice of the modulation frequency. The drop then disintegrates although the acoustic Bond number remains below its critical value. Finally we change the modulation frequency linearly with time, sweeping over a window containing the drop's first eigenfrequency omega(2(res)). After omega(2) has crossed omega(2)((res)), in the range of validity of the inviscid approximation, the drop equatorial radius oscillates between well-defined saturation values. For small modulations the range of oscillation grows linearly with the modulation amplitude. For larger modulations, however, a substantial increase in the oscillation range of the drop equatorial radius is observed in the case of down-sweep, the increase does not occur in up-swceps of the modulation frequency. We compare our results with experimental findings and in particular the so-called jump phenomenon, as well as with experimental and numerical results from the literature. (C) 2002 Elsevier Science Ltd, All rights reserved.