Relevance. Current trends in processing heavy oil with high sulfur content and tightening environmental fuel requirements necessitate hydrocarbon feedstock purification from harmful components such as sulfur. One of the processes for upgrading medium and heavy oil fractions is hydrotreating. Due to the high importance of the hydrotreating in modern oil refining, the use of mathematical models is critically important in the design of new units, optimization of existing ones, and development of catalysts. Aim. This work is devoted to forecasting the operation of an industrial vacuum gas oil hydrotreating unit with a change in the composition of the feedstock and the main control parameters using a mathematical model. Methods. Liquid adsorption chromatography method using the Gradient M unit to determine the composition of vacuum gas oil, gas-liquid chromatography method using the Crystal 2000 M chromatograph to determine the content of sulfur-containing compounds in vacuum gas oil, cryoscopy method in benzene to determine the molecular weight, energy-dispersive X-ray fluorescence spectrometry method to determine total sulfur in vacuum gas oil, pycnometer method for measuring density, quantum chemical research method implemented in the Gaussian program for determining the thermodynamic characteristics of reactions, method of mathematical modeling of chemical-engineering processes Results. The authors have proposed a 12-component mathematical model of the vacuum distillate hydrotreating. The model takes into account most of the reactions of hydrofining, hydrogenation and hydrocracking of heteroorganic compounds, gas–liquid and liquid–solid mass transfer, as well as the effect of catalyst deactivation with coke on its activity. Based on the results of calculations performed using the mathematical model, it can be concluded that the model of the vacuum gas oil hydrotreating reliably reproduces the dependence of the residual sulfur content in the product on changes in the main control parameters of the industrial vacuum distillate hydrotreating unit.