Time dependent evolutions of the profile of free surface (bubble shapes) for a cylindrical container partially filled with a Newtonian fluid of constant density, rotating about its axis of symmetry, have been study. Numerical computations of the dynamics of bubble shapes have been carried out with the sinusoidal function vibration of gravity environment in high and low rotating cylinder speeds. The initial condition of bubble profiles was adopted from the steady‐state formulations in which the computer algorithms have been developed by Hung and Leslie, and Hunget al.