Time-dependent numerical simulations of an axisymmetric ethylene-air diffusion flame are used to quantify the way in which radiation transport affects the development, structure, and dynamics of the flame. The numerical model solves the time-dependent Navier-Stokes equations coupled to submodels for chemical reaction and heat release (ethylene combustion), soot formation, and radiation transport. The soot formation model includes algorithms for soot nucleation, surface growth, coagulation, thermophoresis, and oxidation. The radiative heat flux is found by solving the radiative transfer equation using the Discrete Ordinates Method and includes radiative effects from soot, CO2 and H2O. The model is tested by comparing simulation results with previously published experimental data for a coflowing laminar ethylene-air flame. Simulations of a higher-speed jet at 5 m/s show that radiative heat losses reduce the flame temperature, which decreases the chemical heat release rate. The reduction in heat release rate decreases the volumetric expansion, causing the flame to shrink considerably, and hence changes the overall temperature, species concentration, and soot volume fraction distributions in the flame. The computations show that radiative intensity is attenuated significantly within the heavily sooting region. Radiative heat flux vectors are primarly directed in the radial direction; however, there is a significant axial component that follows the curvature of the sooting region. The computations for an undiluted fuel jet show that heat transfer by radiation dominates transfer by conduction and convection in the heavily sooting regions of the flame.