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This article presents a mathematical process model to simulate the limestone calcination in a single shaft kiln. The process model comprises a set of ordinary differential equations derived from the principle of mass and energy balance, coupled with a discrete particle model based on the shrinking core model. With the computed axial temperature profiles of the gas and solid, the heat loss through the wall as well as the pressure drop is determined. The simulation was done for a shaft kiln with a solid bed height of 13 m and a bed with 70 mm Sauter mean diameter. The width of the particle size distribution was changed to show the influence of the particle size distribution on the process. The results of this study can be transferred directly in the praxis for design, operation, regulation and optimization of the normal shaft kilns.