[Purposes] Slope stability analysis has remained a research hotspot in the geotechnical engineering field. Among the current common methods, the solution of the traditional limit equilibrium method is fast but usually requires the introduction of various assumptions, while finite element and other numerical methods feature slow and cumbersome solution. Thus, the static relaxation discrete element method (DEM) can be combined with cellular automata (CA) to propose a slope stability analysis method that possesses both computational efficiency and accuracy advantages. [Methods] By adopting the spring penalty model, this paper simplified the contact relationship between the faces of block cells to a point-face contact relationship, and the basic mechanical model of a general block was equivalent to a block spring mechanical model. Meanwhile, based on the static relaxation DEM theory, this paper combined the limit equilibrium theory and the CA mechanism to build a slope CA model. Additionally, an analysis program DEMCA Slope was independently developed via the adoption of the computer programming language C++, with two calculation examples analyzed by employing this program. [Findings] In comparing the calculation example 1, the relative error of the safety factor ranges from 6.0% to 7.4%, while in comparing example 2, the relative error of the safety factor is between 8.4% and 13.0%. The failure results demonstrated by the model are basically consistent with the actual ones, and the obtained safety factors are within a reasonable range. [Conclusions] The proposed method holds advantages in both computational efficiency and accuracy, providing a novel insight into the analysis and study of slope stability for further solving slope stability problems.