The design procedure of a process tubular furnace (or fired heater) can generally be divided into three design stages: the preliminary design of furnace, a detailed thermal and hydraulic simulation of the furnace, and final design solution, and the mechanical solution of the furnace (stress analysis, drawings preparation, etc.). The first design stage (the preliminary design of the furnace and cost prediction) is usually connected with a proposal for the customer when only the basic process and furnace design data are usually known. In this design stage, it is appropriate for the furnace designer to not have much detail for a reliable design method. The procedure for the preliminary design of a radiant chamber is usually a main part of such a design method because the radiant chamber represents a basic and dominant part of the modern process tubular furnace. The conceptual (or preliminary) design of the radiant chamber makes up the main part of this process. The presented method is based on standard, time-tested design methods (e.g., the Lobo-Evans method and Belokon's method). It is shown how these standard global design methods can be (for common operating conditions) suitable, generalized, and simplified. It allows for the purpose of the conceptual radiant chamber design the arrangement of the basic heat transfer equation for the radiant chamber. The derived form of the heat transfer equation then allows one to obtain basic process and geometrical radiant chamber characteristics of the given furnace type (cylindrical, box, etc.) iteratively. A developed radiant chamber calculation connected with standard procedures for the design of the furnace convection parts and stack (together with cost predictions) is used, and the method for a quick preliminary evaluation of the influence of the main design and process furnace parameters (dimensions of radiant chamber and convection parts, average heat flux to radiant tubes, absorbed heat in radiant chamber and convection part of furnace, stack size, and fuel consumption) for the total costs was developed. It allows the optimization of the furnace from an investment, operating, or total cost point- of- view in the preliminary design stage of the furnace. The developed method can also be used for the effective solution of the furnace integration into the process. The application of the developed method is demonstrated through a case study - the optimum design of a furnace for a crude atmospheric distillation unit.