The use of axial oscillation generators has become common in constructing inclined wells to reduce the resistance forces of the moving drill string. This study focuses on creating a simulation model to analyze axial vibration processes in a drill string with an axial oscillation tool installed during the construction of inclined-directed wells of a given profile. The model will help evaluate the efficiency of the axial oscillation tool under different operating conditions. The study analyzed and decomposed the drill string into separate elements and developed their mathematical models. These models were created based on assumptions to reduce numerical complexity but accurately describe the interaction between the drill string and the well walls. The soft-string model of the drill string was used as a basis in creating the model, and the interaction of the drill string with the well wall was described by the Stribeck friction model. The rate of penetration of the wellbore was also factored in to simulate the effect of reducing the axial force on the bit. A library of simulation models of drill string elements based on the mathematical model was developed in the Modelica language. These models were used to synthesize a simulation model of the drill string, which can describe the dynamics of a drill string of arbitrary design with one axial oscillation tool located in a well of arbitrary profile. Numerical experiments were then conducted to study the process of deepening a well blowout under various parameters and modes of operation of the axial oscillation tool. The results of these experiments were analyzed to determine the effect of the axial oscillation tool on reducing the resistance forces of the moving drill string