Mathematical modelling of a continuous fluidized-bed reactor has been carried out for non-catalytic gas-solid reactions. The two-phase bubbling bed model has been used and the elutriation phenomenon for the fine particles has been investigated. The feed stream consisting particles with size distribution and reversible or irreversible first-order kinetics can be treated by the model. The reduction behaviour of solid reactants was described by the grain model. A program was developed in MATLAB software for solving the governing equations at conditions of different temperatures and pressures. The model was validated using experimental data and simulation results available in the literature for the iron ore reduction with a gas mixture containing hydrogen [Srinivasan and Staffansson, Chem. Eng. Sci. 45(5), 1253-1265 (1990)]. The mathematical modelling was also used for predicting the extent of reaction for reduction of cobalt oxide by methane.