A numerical study of coupled gas radiation and natural convection in a two-dimensional differentially heated vertical cavity is reported. The momentum and energy balance equations are solved using a pseudo-spectral method. The molecular radiative properties are modelled using the Absorption Distribution Function model and the radiative transfer equation is solved using a ray-tracing method suitable for the two-dimensional flow geometry. The numerical simulations quantitatively confirm the delay of the onset of the transverse instability due to gas radiation predicted by a previous linear stability analysis. Beyond the onset of transverse instability, it is shown that gas radiation can modify significantly the flow regimes, the number of convective cells in the cavity and also the different steps of reverse transition and hysteresis. In the geometry studied here, gas radiation leads to an increase of conductive transfers on the walls of the cavity for small Rayleigh numbers and to the inverse effect for higher values of the Rayleigh number.