Foundations constitute a significant part of the design of civil engineering systems. Geotechnical considerations are particularly important in identifying the conditions leading to instability of shallow and deep foundations under various loadings. In the case the foundation layer is clay, one should identify the conditions leading to failure of clay soil upon loading. The most common way of doing so is to theorize the constitutive behavior of the soil using mathematical equations. In this study, constitutive modeling of clays under monotonic loadings is presented using the Generalized Plasticity Theory. Numerical formulation is summarized in terms of governing equations which are solved for each load step by an explicit integration method which is implemented into a computer program. Elasto-plastic constitutive matrix is derived based upon the inversion of strain-stress relationship without using a yield or a potential function in the model which is used to get the stress-strain incremental relationship. Plastic strains are then calculated using a non-associative flow rule. Subsequently, a number of drained and undrained strain-controlled triaxial tests are simulated to verify the model and its implementation. The related tests are also simulated using the well-known modified Cam Clay model to highlight the capabilities of the Generalized Plasticity model. Simulation results demonstrate the effectiveness and the capability of the model to capture static behavior of normally and overconsolidated clays.