Stability analysis has always been a critical issue in geotechnical engineering. Many of the design works by engineers are actually based on the ultimate condition which can be assessed without the need of the initial condition and sophisticated constitutive models. A brief introduction about the stability analysis will be given in this chapter.

In this chapter, the basic theory about the lower and upper approaches will be introduced. These approaches will then be applied to various types of problems, and the applicability of the lower and upper bound approaches will be illustrated through many types of problems, for which analytical/rigorous solutions are available.

In this chapter, three major stability analysis methods are introduced. Each method will be discussed with many recent findings discussed. Based on the slip line method and extremum limit equilibrium method, the classical slope stability, lateral earth pressure and bearing capacity problems are unified under one formulation. A Fortran code is also provided for the lateral earth pressure analysis based on the limit analysis approach, and this code will be useful to many readers.

In this chapter, the basic theory about the two most important numerical methods in stability analysis are introduced. After that, these two methods are applied to different cases, and some laboratory tests are also used for comparison. In general, it is found that both methods are useful, and each method has its own merits and limitations.

Analytical solutions to most of the geotechnical problems are not available unless the geometry under consideration is highly simplified. For practical purposes, numerical method is indispensable. In this chapter, the numerical methods for some of the stability methods as discussed in previous chapters are elaborated.

In this chapter, the plasticity theory (slip line analysis) and limit analysis will be applied to the bearing capacity problems for illustration. Through these applications, the readers will be able to strengthen their understanding on the various types of stability analysis methods.