Abstract: The critical sliding surface is important for the reinforcement of geotechnical engineering in practice. The present research on critical sliding surface is mostly based on the upper bound theorem, while the theorem and numerical solution of critical sliding surface based on the lower bound theorem or lower bound model have not yet been seen. This article proposes the new critical sliding surface solution theorem based on the lower bound model, and the corresponding numerical solution is provided. The accuracy and reliability of the calculated results as well as the rationality and feasibility of its engineering applications are validated through the examples of an upright slope.