An increasing demand for forest products incites a large number of log transportation operations, which may lead to negative consequences for the soil and the ecosystem as a whole. This paper presents a mathematical model to estimate the soil deformation and compaction processes under the influence of individual components of the skidding system, such as the forwarder, limbs, butts, and tops of tree-lengths in high latitudes, permafrost soil, and forests of the cryolithic zone. The effectiveness of the proposed model was evaluated according to experimental results. Comparative analysis showed that the calculated data differ from the experimental data by no more than 10%. The deformation of the soil by the bunch of tree-length logs occurs due to shearing processes. It has been established that the initial vertical stress exceeds the radial stress by 30–40%. The result of estimating the dependency of the shelterbelt width on the number of tree-length logs showed that the limit values for logs amount to 4–6 units for the mild, medium, and solid soil categories. The obtained results and the developed model will allow for a qualitative and quantitative assessment of the technological impact on the soil during the projecting of maps for logging operations.