The Rayleigh–Taylor instability arises when a heavy fluid adjacent to a light fluid is accelerated in a direction against the density gradient. Under this unstable configuration, a perturbation mode of small amplitude grows into bubbles of the light fluid and spikes of the heavy fluid. Taylor discovered the steady state motion with constant velocity for a single bubble or periodic bubbles in the Rayleigh–Taylor instability. Read and Youngs studied the motion of a randomly perturbed fluid interface in the Rayleigh–Taylor instability. They reported constant acceleration for the overall bubble envelope. Bubble merger is believed to cause the transition from constant velocity to constant acceleration. In this paper, we present a numerical study of this important physical phenomenon. It analyzes the physical process of bubble merger and the relationship between the horizontal bubble expansion and the vertical interface acceleration. A dynamic bubble velocity, beyond Taylor’s steady state value, is observed during the merger process. It is believed that this velocity is due to the superposition of the bubble velocity with a secondary subharmonic unstable mode. The numerical results are compared with experiments. ©1996 American Institute of Physics.