<p>Loess-mudstone landslides are common in the Loess Plateau. Investigations into the mechanical theory of loess-mudstone landslides have become a challenging undertaking due to the distinctive interfacial properties of loess-mudstone and the unique water sensitivity characteristics of mudstone. Hence, it is imperative to develop innovative mechanical models and mathematical equations specifically tailored to loess-mudstone landslides. In this study, we analyze the fracture mechanism of the loess-mudstone sliding zone using plastic fracture mechanics and develop a unique fracture yield model. To calculate the energy release rate during the expansion of the loess-mudstone interface tip region, the shear fracture energy <i>G</i> is applied, which reflects both the yield failure criterion and the fracture failure criterion. To better understand the instability mechanism of loess-mudstone landslides, equilibrium equations based on <i>G</i> are established for tractive, compressive, and tensile loess-mudstone landslides. Based on the equilibrium equation, the critical length <i>L</i>_c of the sliding zone can be used for the safety evaluation of loess-mudstone landslides. In this way, this study proposes a new method for determining the failure mechanism and equilibrium equation of loess-mudstone landslides, which resolves their starting mechanism, mechanical equilibrium equations, and safety evaluation indicators, thus justifying the scientific significance and practical value of this research.</p>