The scientific and technical problem of modeling gas-abrasive wear of an axial compressor blade row is investigated. The objectives of the study are to determine the current state of this area of research and develop a gas-abrasive wear calculation methodology. Attention is focused on the verification of the computation method based on the published results of experiments with gas-abrasive erosion in the round pipe swivel channel. A detailed review of the domestic and foreign literature is carried out. The study is aimed at predicting the extent of blade row gas-abrasive wear using the computational fluid dynamics methods. A step-by-step description of the algorithm for solving the problem by a numerical method with a historical review of erosion models developed by other researchers is given. An algorithm for calculating gas-abrasive wear in an axial compressor is elaborated, and possible algorithms for calculating the fluid dynamic characteristics of a compressor subjected to gas-abrasive wear are analyzed. The study results can be used in designing the axial compressors of gas turbine units that operate under polluted air conditions. Thus, by using the numerical method, it is possible to carry out a qualitative and quantitative analysis of an axial compressor’s wheel space gas-abrasive wear. The main contribution in the erosion wear computation accuracy is introduced by a correct calibration of the erosion model. Therefore, to obtain adequate results, reliable experimental data on determining the properties of interaction between the eroding particles and the wall are required.