A study on saturation induced soil instability is presented. A constitutive model for unsaturated soils is linked to a theoretical approach able to deal with mechanical instability of fully saturated geomaterials. The theoretical approach is therefore extended to the more general case of partially saturated soils. The controllability of generalised loading tests is then considered, focusing on oedometric tests at varying water content. It is shown that instability phenomena, such as collapse at constant axial loading, can be described. In addition, it is discussed how oedometric instability modes can be interpreted as possible compaction band bifurcations. Finally, similar results are reported for the simpler case of isotropic state of stress, defining the most relevant material parameters in determining such instability modes.