Abstract A first-principles model for gas-fluidized bed based on the so-called “two-fluid model” (TFM) has been developed. In the TFM approach, both phases are considered to be continuous and fully interpenetrating. The equations of mass, momentum and thermal energy conservation, supplemented with the necessary constitutive equations, have been solved by a finite-difference technique on a mini-computer. The computer model calculates the porosity, the pressure, the fluid phase temperature, the solid phase temperature and the velocity fields of both phases in two-dimensional Cartesian or axi-symmetrical cylindrical coordinates. Contrary to previous modelling work, all important terms have been retained in the transport equations. As a test of the theoretical model, the phenomena associated with the formation propagation and eruption of a single bubble in a cold-flow two-dimensional air-fluidized bed with one central orifice have been calculated theoretically. The calculation was done for mono-sized spherical solid particles with a diameter of 500 μm and a true density of 2660 kg/m 3. Our preliminary calculations indicate strong leakage of bubble gas into the emulsion phase, especially during the initial stage of bubble formation. In its present state, the model does not correctly display all the details associated with the propagation of bubbles in gas-fluidized beds. The further development of the model, both from a physical (bed rheology) and mathematical (finite-difference approximations) point of view, seems highly desirable.