Finite element methods are largely used in solving nonlinear geometrical and material problems. But standard finite element methods are ineffectively in handling extreme material deformation

such as cases of large deformation and severe mesh distortion problems in computation. Arbitrary Lagrangian-Eulerian (ALE) methods incorporate the advantages of Lagrangian and Eulerian methods and overcome their disadvantages. The methods can solve many problems which can be solved difficultly by Lagrangian and Eulerian methods. Based on ALE finite element methods and fundamental theory of elastoplastic large deformation

the soil slope stability problems of a simple soil slope and a complex soil slope with weak layer under self-gravity in geotechnical engineering are analyzed as the illustrative cases. The computational results show that the deformation behaviors of slope sliding and the critical slip plane can be defined clearly from the deformed shape obtained by ALE finite element method. The results show that the arbitrary Lagrangian-Eulerian (ALE) methods can effectively analyze the stability of soil slopes and be applied to the elastoplasticity analysis of geotechnical engineering.