The application of the theories of elasticity and plasticity to stability problems in soil mechanics is discussed and it is concluded that the limit equilibrium method of analysis is preferable to either of these two theories for the solution of the problem of the stability of earth slopes. The circular arc analyses are developed in detail and comparisons are made between the friction-circle method and the method of slices. Stability coefficients are then obtained to facilitate the application of the method of slices to the determination of the factor of safety of earth slopes in terms of effective stresses. Charts giving factors of safety are also obtained for the special case of rapid drawdown of an earth slope. Finally, a new limit equilibrium method of analysis is developed that allows the calculation of the factor of safety for a sliding surface of any shape through a section of any profile and pore-pressure distribution. Examples have been calculated to illustrate this new method.