This paper presents a steady state mathematical model of a direct-fired continuous reheating furnace. The model was developed to identify the design and operating parameters that significantly affect furnace performance. The actual furnace, which requires a full three-dimensional mathematical description, is approximated two-dimensionally. The fuel and air streams enter the furnace in such a way that the load is heated by direct impingement of a turbulent diffusion flame jet. The details of the combustion space model, which includes a turbulence model and a discrete-ordinates representation of the radiation field, are provided. In addition, the results of parametric studies, in which the fuel firing rate and the load and refractory emissivities were varied, are provided.