This book focuses on recent developments in mathematical modeling of bifurcations, instabilities, localization and post-localization phenomena that are taking place in geomaterials (soils and rocks). The reader is introduced to the basic concepts of contemporary non-linear continuum geomechanics bifurcation and constitutive theory for ordinary and "enhanced continua" (second gradient and Cosserat continua). Within this frame, the finite element method of analysis is adapted and further developed in order to address boundary value problems that involve post-localization modeling.