The relevance of the work is justified by the need to improve the technical and economic indicators of well construction based on forecasting and preventing drilling tools sticking due to the narrowing of an open well bore in the intervals of transversely isotropic rocks. A mathematical model of elastic-viscous-plastic displacement of the walls of inclined and horizontal wells has been developed during the narrowing of the open borehole due to rock creep in the intervals of transversely isotropic rocks. In the program developed based on this mathematical model, the calculation of the elastic-viscous-plastic displacement of the walls of an obliquely directed and horizontal well in the reservoir of argillite from the Western Siberia deposit was carried out. As a result of the calculation, it was established that after opening the rock with bits, the cross-section of the open borehole due to the rock creep eventually takes the form of an ellipse, the small axis of which is in the plane of the upper wall of the well and decreases with time.
