The primary focus in this research is on proposing a methodology for modeling of discrete crack propagation in geomaterials such as soil, rock, and concrete. Structures made of such materials may undergo damage due to several reasons. Here, mechanical loading and chemo-mechanical interactions that result in degradation of strength parameters are considered as the sources of damage initiation. Both tensile and compressive cracks are investigated. For analysis of crack propagation, two different methodologies are employed; the Constitutive Law with Embedded Discontinuity (CLED) and the Extended Finite Element Method (XFEM). The CLED approach is enhanced here to describe the discrete nature of crack propagation. This is done by coupling the CLED with explicit modeling of crack path using the Level-Set method. The XFEM is used as a verification tool to check the results from CLED analysis. An algorithm is proposed for crack initiation and propagation that results in stable and a mesh-independent solution. The CLED approach is further improved by developing the return-mapping and closest-point projection algorithms. Extensive numerical investigations are conducted that include mode I cracking in a three point bending test, mode I cracking in notched cantilever beam, mixed cracking mode in a plate subjected to shear and tension, and a mixed mode cracking in a notched beam under four point loading. For frictional interfaces, the shear band formation in a sample subjected to bi-axial compression and the shear band formation in a geo-slope are studied. The thesis also addresses the topic of the response of unsaturated cohesive soils undergoing an infiltration process. The problem is approached within the framework of Chemo-Plasticity. It is assumed that the complex chemo-mechanical interactions are the controlling factors for degradation of strength parameters during this process. A return mapping integration scheme is developed and the approach is employed to investigate the stability of a geoslope subjected to a heavy rainfall. Analysis of shear band formation is further investigated in the context of sedimentary rocks. The microstructure tensor approach is used to describe the inherent anisotropy in this class of materials. The orientation of the shear band is defined by invoking the Critical Plane approach and the closest-point projection algorithm is developed for numerical integration of the governing constitutive relations. The model is used along with CLED for analysis of the mechanical response of Tournemire argillite. It is shown that the friction between loading platens and sample can play an important role in the process of shear band formation and the associated assessment of the ultimate load. A mesh-sensitivity analysis employing the CLED framework is also conducted here. The research clearly demonstrates that the discrete representation of crack path propagation is essential for an accurate analysis of failure in various engineering structures. It is shown that if the classical smeared Constitutive Law with Embedded Discontinuity is enhanced to simulate the discrete nature of the damage process, it can yield very accurate results that are virtually identical to those obtained from discrete approaches such as XFEM.