A numerical approach for predicting multi-dimensional reacting flows is presented. The various interacting processes which occur during combustion are considered: turbulent transport, chemical reaction, and radiative heat transfer. The formulation is based on time-averaged transport equations. Turbulent transport is modeled with the k-epsilon turbulence model, chemical reactions are considered using the eddy dissipation concept (EDC), and radiative heat transfer is modeled with the discrete ordinates method. The EDC includes influences of both local turbulence and finite-rate chemical kinetics on the reaction rates, and is applicable to general, n-step, elementary reaction mechanisms. The model is applied to two swirling natural gas flames. Predictions are presented for several detailed and reduced reaction mechanisms including the 279-step GRI-Mech. Results indicate that the use of intermediate and detailed reaction mechanisms with the EDC significantly reduces uncertainty associated with simple one-and two-step chemistry, but also that k-epsilon model underpredicts turbulent transport in the considered flames.