As a technical and economical alternative to foundations on piles, but also to shallow foundations on improved soil, in recent decades a high number of soil improvement methods have been developed and established. Many of these methods use non-reinforced, cylindrical load bearing elements. A very common application of stabilizing columns is the improvement of a few meters thick soft soils below dams and embankments. But especially for this application, many failure cases are documented worldwide. In the contribution the substantial content and results are presented for investigation, testing and further development of methods for evaluating the slope stability. After a description of the problem and consequential tasks the contribution contains main results of the investigations of international sources with the stepwise development of analytical solutions. Next to the in practice well- known approaches for gravel columns, less common approaches from Scandinavia are explained. The contribution is completed with a presentation and discussion of an illustrative example, taking into account a number of different failure modes of the columns and the surrounding soil. The example was compared and validated with a 3D Model using the Finite Element Method.