Historically it is known that many failures in earth dams and natural slopes can be attributed to the phenomenon of sand liquefaction, caused by dynamic loads generated by earthquake shaking or other rapid loading, such as blasts. When liquefaction occurs, the strength of the soil decreases and its ability to support foundations for buildings and bridges is significantly reduced. Liquefied soil can also exerts higher pressure on retaining walls, which can cause them to tilt or slide, yielding settlement of the retained soil with risks of destruction of structures on the ground surface. The term liquefaction has actually been used to describe a number of related phenomena, which produce similar effects but whose mechanisms are quite different in nature. These phenomena can be divided into two main categories: flow liquefaction and cyclic mobility. Flow liquefaction is a phenomenon in which the static equilibrium is destroyed by static or dynamic loads in a soil deposit with low residual strength. Failures caused by flow liquefaction are often characterized by large and rapid movements. Cyclic mobility, on the other hand, is a liquefaction phenomenon triggered by cyclic loading, occurring in soil deposits with static shear stresses lower than the soil strength. Deformations due to cyclic mobility develop incrementally because of static and dynamic stresses that exist during an earthquake. The rising of tailing dams using the upstream construction technique can lead to static liquefaction failure if the rate of construction is sufficiently high to cause excess pore pressure to develop in the tailings. The liquefaction response is observed for loose specimens when the shear stress exhibits a peak followed by a phase of apparent softening that, in undrained loading, is associated with the tendency of the material to contract (densify). For some initial loading states, the descending part of the response is followed by an increasing part, leveling-off eventually when the material reaches the final, critical (steady) state. In this thesis, the modeling of the phenomenon of static liquefaction is carried out considering the constitutive models proposed in the literature by Juárez-Badillo (1999b) and Gutierrez & Verdugo (1995). The latter, mainly after introducing the assumption that some material parameters are stress dependent and not simple constants, as in the original version, produced good matching between experimental and predicted results, in spite the simplicity of the mathematical formulation.