The purpose of this dissertation is to contribute to the detection of the onset of geomechanical instabilities in sands under dry/drained and saturated/undrained conditions. ln order to accomplish this objective, a framework for detecting instabilities based on either a mathematical concept (i.e., loss of uniqueness - bifurcation) or physical one (i.e., Hill 's instability) is generated to derived criteria applicable to the most common instabilities: localized drained instability in dense sands (shear bands), diffuse undrained instability in loose sands (Iiquefaction) and diffuse drained instability in loose and dense sands (debris flow). Each one of these three instabilities is studied independently. The criteria are compared against experimental results available in the literature, and reasonable agreement is achieved. From a practical perspective, the contributions of this work expand the repertoire of potential instabilities that have been reported in case studies of puzzling slope instability failures under drained and undrained conditions. Alfonso Mariano Ramos Cañón