1. There is no correct or wrong method. Unless you 're using the FE method, all use the limit equilibrium principle, and are bound by its restrictions. 2. Apart from very simple cases, the problem of calculating the 'factor of safety' is indeterminate. Therefore assumptions have to be made to render the problem statically determinate and solve it. Different methods use different assumptions. 3. The classical Fellenius method is the simpler. He assumed that the interslice forces are zero. The calculated FOS is generally bigger than the one calculated with the ither methods. 4. Bishop's simplified is the one I use at first, because it gives good results fast. He assumed that the interslice shear force is zero. In his rigorous method he iterates to find the values of the interslice shear forces, but this is not convenient. 5. The Morgenstern-Price and the Spencer methods assume a relationship X=lamda*E. I think that the algorithm given by Spencer is better and easier to understand. The methods are rigorous in the sense that all forces can be calculated, and all the slices satisfy force and moment equilibrium. Since this is numerical analysis, always check the force and moment imbalance, because this will never be zero. Depending on the way the method is programmed, if lamda turns out to be positive, it means that the slope moves uphill, which is unacceptable. If it is zero, than you have a Bishop's simplified solution. 6. Sarma's 1973 (rigorous) method assumes that X=lamda*Q, where Q is calculated. 7. A very useful reference is Geotechnique, year 1979, Sarma. 8. Unless you 're an expert in a particular method, I suggest you use more than one.