The penetration of a front of light fluid into a heavy fluid in a Rayleigh–Taylor unstable flow is studied by using a model that simulates the competition among the bubbles formed in the interface when the density ratio of the two fluids is very large. Several different initial conditions have been considered, and it is found that the front moves with constant acceleration. The values obtained for the acceleration of the front are in very good agreement with experimental results obtained by Read [Physica D12, 45 (1984)].