Abstract: Based on the second-order work criterion and bifurcation analysis, the framework for predicting the onset of diffuse instability and strain localization are proposed to study the instability of soils under K₀-consolidated undrained loading conditions. The analysis shows that the diffuse instability occurs in triaxial tests while the strain localization does not occur. The onset of diffuse instability relies on the initial void ratio of the specimen, and if the soil is dense enough, the soil specimen keeps stable until plastic limit due to the phase transformation. Under the plane strain conditions, the diffuse instability precedes the strain localization, and with further loading, the diffuse instability transits to strain localization. The inclusion of the non-coaxial plasticity flow rule has significant influence on the onset of strain localization, and the predicted results agree well with the experiments only if the non-coaxial flow rule is considered, while it shows no influence on the prediction of diffuse instability.