Interaction peculiarities of a single unit bored pile with the surrounding rock mass under the horizontal load effect, as well as loss mechanism of piles bearing capacity, are considered. The article presents the numerical modeling results and a method developed on their basis for calculating piles in rocky soils under the horizontal load effect under the spatial elastic-plastic problem conditions, with the account of the contact behavior between the pile and the rock mass. The study of the single unit bored pile interaction and the surrounding rock mass under the horizontal and moment loads effect was carried out based on the numerical models’ analysis of the piles and the surrounding rock mass in a spatial setting using the finite element method. The use of regression analysis methods made it possible, to obtain parametric equations, based on the numerical modeling obtained results, that connected the studied response functions (bearing capacity and horizontal displacement of the pile) from preselected independent factors reflecting the geomechanical properties of the body and the design piles peculiarities. The developed calculation method allows at the preliminary design stage to estimate the horizontal pile displacement value, as well as its bearing capacity. Also, using the proposed technique, it is possible to make a piles load test schedule, which can be used in the field observation preparation at the design stage. The relevance of the topic is due to the fact that in modern construction practice, bored piles are used to transfer to the foundation significant loads, on the rock foundation from structures for various purposes, including transport (bridges and overpasses piers’ foundations, etc.).