A mathematical model is presented for the swirling unstaged natural gas flame. The performance of the model is critically assessed by comparison with a detailed set of experimental measurements. The model makes use of a conserved scalar approach. Turbulence is modelled using k-epsilon model with turbulence chemistry interaction accounted for using a two parameter presumed p.d.f. Radiative heat transfer is treated by means of the discrete transfer method and chemistry models making use of the “mixed is burnt” and partial equilibrium assumptions are evaluated. Numerical solution is by means of a collocated finite volume approach in a general non-orthogonal curvilinear coordinate system. It is seen that predictions to reasonable engineering accuracy can be obtained, with the partial equilibrium model offering some advantage over fast irreversible chemistry. Recommendations for future development are given.