Gas-liquid flow in packed towers is commonly encountered in the chemical and processing industry. A continuum model is developed based on the volume-and-time averaging of multiphase flows in isotropic rigid porous media/packed columns. Closures are presented for the evaluations of the extra surface/intrinsic phase integral terms. Both inertia and inter-phase interactions are retained in the Volume averaged (Navier-Stokes) equations. These governing equations are solved for fully-developed axi-symmetric single and gas-liquid two phase flows in highly porous packed towers. It is found that the dispersion term is present in the continuity equation as well as the momentum equations. Numerical simulations with the models show that the volume-and-time averaged equations can predict the velocity, phase hold-up and pressure drop quite well for up to the loading point for gas-liquid counter-current flows.