Introduction. An analysis of existing studies shows that surface translational landslides on grassy slopes, along with other hazards, contribute to soil erosion and harm grazing lands. The formation of a landslide body is based on the stress-strain state of a sod and its subsequent destruction when liquid precipitation falls on the slope. The most accurate method for studying such a landslide process is mathematical modeling. The fundamental disadvantages of all existing mathematical models in this area is an incomplete system of equations that describe the stress-strain state of a surface layer of a slope during precipitation. Materials and methods. This study uses a mathematical modeling methodology based on theory of generalized functions. Results and discussion. The developed mathematical model is reduced to a system of partial differential equations. This system describes the stress-strain state of a sod, caused by the external stress field and the stress field of the swelling. The study of this system of equations and the resulting final expressions showed that the superposition of these stress fields leads to a weak bending of a potential landslide body. Separation of this body from the slope occurs under the influence of general stretching, leading to its destruction. As a result, it turns into a lumpy, loose landslide body that moves down the slope. Conclusion. The mechanism of a surface translational landslide with a sod on straight slopes of mountain territories during atmospheric precipitation has been revealed. According to this mechanism: 1) the external stress field forms a potential landslide body; 2) under the influence of the liquid precipitation, the stress field of the swelling is formed. The superposition of these stress fields leads to a movement of the landslide over a short distance. Suggestions for practical application and direction of future research. The research results can be used to prevent landslides with a sod on straight slopes of mountainous territories during precipitation. Further research directions should be related to an improvement of mathematical models of the stress-strain state of a sod under different slope topography.