A model taking into consideration flow compressibility and gas-solid reactions in a packed bed is presented in this paper. The isothermal chemical reaction has two effects on the flow of a gas mixture: (i) the creation of a sink (or a source) due to reaction, and (ii) the density change of the gas mixture due to reaction. A one-dimensional numerical solution for transient flow of a gas mixture in a packed bed having isothermal gas-solid reactions is carried out. The numerical results show that the velocity profile obtained from this coupled model differs greatly from the existing non-coupled model, not only in magnitude but also in the velocity variation trend in the packed bed. A coupled mode, including only the mass dissipation of gas or generation effects of gas but neglecting the density change of a gas mixture, leads to an extra sink of gas mass dissipation or a source of gas mass generation, which depends on the molar mass of gas species. It is shown that the density change of the gas mixture in reaction cannot be ignored, especially in the case that there is observable difference in the molar mass between reactive gas and inert gas. It is also found that concentration profiles obtained from the coupled models differ greatly from that obtained from a non-coupled model.