One of the main causes of damage to the elements of coal-fired boilers installations, leading to breakdowns and, consequently, a shutdown of the block, are erosive processes. Unfortunately, there is not much research conducted on dust erosion of the dust ducts supplying the air–dust mixture to the burners. The problem of erosion of the dust ducts supplying the pulverized coal–air mixture to the burners was presented in this paper. This study was performed for the preliminary feasibility design. The destruction of the material of the dust ducts results in a failure due to erosion, resulting in the mill being shut down from an operation, which in turn may lead to the shutdown of the power plant unit. Therefore, it is important to identify places exposed to pulverized coal erosion. In order to perform calculations, numerical modeling in the commercial program Ansys.Fluent (Ansys Fluent, Computational Fluid Dynamics, Ansys Inc., Pittsburgh, PA, USA) was used. The parameters obtained as a result of laboratory tests were used in the erosion model. The places where erosion is expected are indicated. The highest erosive wear occurred for the M3 mill dust ducts for the case coal 1 and amounted to 45.6 mm/5200 h. On the other hand, the lowest erosive wear occurred for the M2 mill dust ducts powered by coal 3 and amounted to 20.9 mm/5200 h. The identification of places where erosion is expected can be used to protect these places from erosion adequately. Nevertheless, a dispersion threshold should also be placed where there is a high concentration of pulverized coal contributing to increased erosion. The numerical calculations provided information on the velocity of the medium and the behavior of the dust in the dust duct. The numerical calculations also provided information on where dust lacing has occurred. It was shown that coal dust particles with a diameter greater than 100 µm largely erode the dust duct’s wall. A model is presented for the calculation of the erosion process to be used in the dust ducts of the power plant.