The distribution of bubbles and the rate of coalescence of bubbles are important factors in the overall behaviour of fluidized beds. A simple model capable of predicting bubble distribution and bubble-size distribution is most desirable. Stages in the development of such a simple model are presented. Early studies examined coalescence and related bubble properties in two-dimensional beds and led to the formulation of a simple computer model for two-dimensional beds. The work was then extended to three-dimensional beds covering the following cases: (i) a single orifice; (ii) a row of orifices in a line and (iii) orifices arranged in a plane. Reasonable agreement with experimental data was obtained for cases (i) and (iii), there being no data available for (ii). The present program is probably adequate for engineering purposes, so far as the prediction of bubble sizes and bubble distribution is concerned, in fluidized beds without internals, although some qualifications are still necessary.