The analysis of slope stability is one of the most important problems in engineering geology. There are numerous methods developed for solving it within the frames of the limit equilibrium theory. As a rule, these methods are based on the following assumptions.

The failure mechanism is assumed to be a slip of a soil mass with respect to a stable part of the slope. The boundary between the sliding soil mass and the stable soil is called a slip surface.

The shear resistance along the slip surface is calculated under static conditions. The Coulomb failure criterion is satisfied along the whole surface.

The actual shear stress obtained by the calculation is compared with the ultimate shear resistance, and the result of the comparison is expressed as a factor of safety K. For a particular slip surface, the factor of safety K is such a number that if the strength parameters (the internal friction angle and the effective cohesion) along the whole surface are made K times smaller, then the potential sliding soil mass will be in the limit equilibrium state. The factor of safety of a slope is a minimum factor of safety for all potential slip surfaces which satisfy given restrictions (the restrictions are usually defined by the method of analysis).

The real slip surface is three-dimensional. However, most methods of analysis, including the SLOPE software, assume a plane strain hypothesis where the slip surface is cylindrical with its generatrices parallel to the slope surface and the problem comes down to finding a critical directrix called a slip line. This approach is based on the hypothesis that ignoring the spatial character of the phenomenon has little effect on the stability factor of safety and affects only the strength factor of safety.

Various, usually fairly limited, classes of potential slip lines are used (such as circular arcs or logarithmic spirals). However, it is obvious that the limitations of the slip surface configuration must be minimal for essentially nonhomogeneous slopes and complicated groundwater conditions taken into account by the software.

The algorithm of analysis implemented in SLOPE is based on a procedure suggested by V.Fedorovsky & S.Kurillo, which uses the method of variable level of shear-strength mobilization (MVLM).

Moreover, the following classic methods of the slope stability analysis are also implemented in the software:

- Fellenius
- Bishop simplified
- Spenser
- U.S. Army Corps of Engineers method No 1
- Lowe-Karafiath
- Janbu simplified
- Janbu corrected

The description of these standard methods is given in most books on slope stability analysis.

It should be noted that the Fellenius, Bishop simplified and Spencer methods allow to analyze circular slip surfaces only.