In the Russian Federation, a significant part of the forest fund is located on the permafrost. Permafrost forests play a global ecological role by depositing large amounts of carbon. However, when a forest reaches the age of obsolescence, this carbon is released into the atmosphere as it decays. Therefore, from an ecological point of view, permafrost forests should be cut down when they reach the age of maturity, in compliance with the requirements for their restoration. Many of these regions have large reserves of mature and overmature commercial forests, and a significant portion of these reserves are located in places difficult to access, not only in relation to the development of road networks, but also on the terrain. At present the overwhelming majority of timber felling in Russia is performed with the help of modern machinery complexes, which mainly include wheeled forestry machines of different layout and purpose (harvesters, forwarders, skidders, etc.). With the help of special technical solutions, such as winches integrated into the transmission, or self-propelled winches (T-winch, ROB), these machines can be successfully operated on fairly steep slopes. The problem of negative effect of wheeled forest machines and skidding systems based on them not only remains actual, but becomes even more urgent, as the ecosystems of mountain forests, forests on slopes of hills, etc. are the most vulnerable and exposed to water and wind erosion. The developed mathematical model, which allows evaluating the dynamic impact of a wheeled forestry machine (skidder system) on the ground while working on slopes with taking into account the main technical and technological factors, is presented in the article