A one-dimensional mathematical model of particulate solids fluidization based on the theory of Markov chains is proposed. Transition probabilities that form the matrix and control the migration of particles over the bed are subdivided into two types, convection and diffusion. The convection transition probabilities depend on the local particle concentration in cells of the chain and mainly define the bed expansion at certain hydrodynamic conditions. The diffusion transition probabilities form particle concentration distribution over the bed height. On the basis of the model, the heat exchange between gas and particulate solids is described. The batch fluidization model is generalized to the case of continuous fluidization that allows predicting a connection between throughput and hold-up, as well as particle residence time distribution in a bed. Some aspects of the approach are verified experimentally.