Self‐consistent nonequilibrium fluid models of both the two‐dimension (2D) and one‐dimension (1D) are presented. In the 2D simulations, the models evaluate the quantitative effects of both radial and axial flow dynamics inside a cylindrically symmetric parallel‐plate geometry. The 1D model assumes that the radius of the electrode is much larger than the electrode gap and the moment distributions are uniform along the radial direction. The models are based on the first three moments of the Boltzmann equation and Poisson’s equation. Radio frequency (rf) glow discharge simulations from those two fluid models are presented and compared in this study. The comparisons are presented in terms of plasma density, electric field, mean energy, and ionization rate. Results of the 1D fluid model are close to those at the center of the reactor from the 2D simulations. Nonuniform profiles along the radial direction are obtained from the 2D simulations due to the radial dynamics. Higher electron mean energy in the middle region of the radial sheath is observed. The maximum ionization rate is located in the radial sheath region and agrees with the experimental observation.