In this paper we study the fluidization of 1204 spheres at Reynolds numbers in the thousands using the method of distributed Lagrange multipliers. The results of the simulation are compared with an experiment. This is the first direct numerical simulation of a fluidized bed at the finite Reynolds numbers encountered in applications. The simulations are processed to give straight lines in log–log plots leading to power laws as in the celebrated experimental correlations of Richardson & Zaki (1954). The numerical method allows the first direct calculation of the slip velocity and other averaged values used in two-fluid continuum models. The computation and the experiment show that a single particle may be in balance with respect to weight and drag for an interval of fluidizing velocities; the expectation that the fluidizing velocity is unique is not realized. The numerical method reveals that the dynamic pressure decreases slowly with the fluidizing velocity. Tentative interpretations of these new results are discussed.