In this work, the boundary element method combined with the fourth order Runge–Kutta scheme as time integrator is used to simulate the dynamics of an acoustically levitated axisymmetric liquid drop. For a given set of dimensionless parameters—wavenumber, Bond number, and acoustic Bond number—the drop dynamics in an acoustic field is studied in terms of the shape oscillation and the translational motion of the drop. The shape oscillation of the drop is characterized by using the equatorial radius and its rate of change as two phase variables. Fixed points on this phase plane represent the static equilibrium shapes. The translational motion is characterized by using the position and the velocity of the drop centroid as two phase variables. The fixed points on this phase plane represent the equilibrium positions of the drop in the acoustic field. It is found that fixed points corresponding to both translational and shape oscillations undergo saddle-node bifurcations with the acoustic Bond number as a parameter. These saddle-node bifurcations define an upper and a lower limit on the acoustic Bond number that can be used in acoustic levitation. We also investigate the coupling effect between the translational oscillation and the shape oscillation. It is found that owing to the order-of-magnitude difference between the period of translational oscillation and that of shape oscillation the coupling effect is only significant at the boundary of the trapping region. ©1997 American Institute of Physics.