Soil densification may lead to buildup of excess pore water pressure, which causes the soil to lose its strength and resulting in, possibly, the instability of the system. For this reason the concept of compact state, defined as the state that all granular will eventually assume when subjected to large number of stress cycles, is postulated.  The proposed constitutive model used in describing the stress-strain characteristics of the soil is the extended CANAsand model: an elasto-plastic material with a non-associated flow rule along with the concept of bounding surface plasticity possessing ultimate state and compact state. The model is capable of realistically simulating stress-strain behavior of sands under monotonic and cyclic, drained and undrained loading conditions. The numerical results indicate that samples looser than the critical void ratio have a very high potential to collapse upon loading. Deposits denser than the critical void ratio could also liquefy as the tendency to contract exists even in these deposits. Dilatation manifests itself only if the deposit is subjected to large amplitude cyclic loading. Such high stress loading cycles are not likely to occur very often in nature.  The present research focuses on the modification of CANAsand model (to incorporate the compact state) and its application to two particular problems in the domain of large displacements. These are: (i) The quasi-static behavior of seabed sand deposit under the action of a standing wave is investigated. The simulation results of seabed sands are given and the influence of the wave amplitude and the wave length for a wide range of void ratio are discussed. (ii) An upper bound solution of the sand blow phenomenon that has received attention of the geotechnical and earthquake engineers is also presented. The application of the ID (Integro-Differential) technique for plane strain problems is discussed. Some numerical experiments are carried out by the computer in order to provide an assessment of the performance of a system composed of a surficial clay layer and supported by a deposit of sand