Multiphysical nature is characterized by complex phenomena involved in instabilities, strain localization and bifurcation in landslides, borehole instability in nuclear waste disposal and drying cracking. This chapter provides an overview of a series of phenomenain geomechanics which qualify as instabilities/failures of various kinds in geomaterials. It focuses on the classical phenomena associated with purely mechanical loading induced instabilities and their criteria and implications to expand into an array of non-classical multiphysics instability phenomena. Local stability is usually tested in a materials laboratory on a uniform specimen, or in a mathematical model, for a single material point. Global stability can rarely be tested on a large scale, but attempts have been made to monitor known landslide sites or earthquake source sites, or to conduct large liquefaction experiments. The chapter presents a case study of two landslide slip surfaces at Diao Jiao Zui and Qian Jiang Ping sites in the three Gorges area, China.