A three-dimensional steady-state mathematical model of a rotary calcining kiln for the petroleum coke is presented. The model takes into account all the physical phenomena of interest, from gas flow, heat transfer, volatile matter and coke dust evolution and combustion, to the granular bed motion and the thermal effects of the refractories. The model is built in modular form with several submodels coupled together. This methodology facilitates the construction of the model and its use. This article gives a detailed mathematical description of the model. A complete simulation is presented, and the results are discussed. Data coming from an industrial kiln in operation are used for validation, and the results show that the model can be a useful tool for solving problems of kiln operation or design.