Abstract: By summarizing years of theoretical research achievements gained by the author and his research team members, the analysis methods to study the instability and behaviors capacity of soils were concluded from two aspects, sands and saturated soft clays, respectively. Under drained loading conditions, the deformation of dense sand may accompany with strain localization before reaching the plastic limit, but that of saturated loose sand may accompany with diffusive instability. The phenomenon of strain localization in plane strain tests and true triaxial tests of sands was studied by the bifurcation analysis based on the three-dimensional non-coaxial plasticity theory. Further, the strength properties and strain localization of anisotropic sands were analyzed, including the strain localization analysis using a state-dependent constitutive model for sands. In addition, the feasibility to overcome the mesh-size dependence problems with the homogenization procedure and the non-local regularization was explored in the finite element analysis. By using the state-dependent constitutive model, the elasto-plastic finite element procedure accounting for the strain localization of drained sands and diffusive instability of saturated sands was proposed. For the saturated soft clays, a simplified formula for calculating their anisotropic undrained shear strength was put forward based on the critical state theory, and the undrained shear strength degradation was also predicted according to the plastic strain accumulated during cyclic loading. Additionally, a rational static and dynamic finite element analysis method for analyzing the saturated soft clays with low permeability was proposed, which effectively solves the problem caused by the incompressible condition. The upper