Abstract: The two - fluid model equations describing gas and solid flow macroscopically in a dense fluidized bed were derived from the well known Navier - Stokes equations of the gas and the Newtonian equations of a single particle using the rigorous volume - averaging method. Four parameters of the model equations were obtained. The model equations could be simplified to Gidaspows, Blakes and Davidsons equations, which verified our two - fluid model equations tentatively. The model equations were solved by means of the modified IPSA technique based on finite - volume method. Numerical computations were made for the gas and solid flow in a two - dimensional jet fluidized bed containing fine sand, millet or binary mixture (fine sand and ash -agglomerate). The numerical results are in good agreement with experimental and reported data in the literature.