The purpose of this study is to perform a complete finite element (FE) simulation of the suction bucket foundation in clay using advanced soil constitutive model to establish the failure envelope of the suction bucket foundation. Firstly, the Hardening Soil (HS) model is used to analyse the centrifuge tests of suction bucket foundation in normally consolidated clay under different monotonic combined loadings by FE method. The comparisons between testing and simulated results verify the effectiveness of the FE analysis using the HS model. Then, a large number of FE analysis is performed by radial swipe tests, and further extended to the failure mode of V-H-M (vertical force-horizontal force-bending moment) space. Based on this, the failure envelope on the H-M plane, the V-H plane, and the three-dimensional failure envelope surface in the V-H-M space are described. The results show that the H-M failure envelope is similar to an inclined ellipse; the effect of vertical load on the inclination of the H-M failure envelope can be ignored; the size of the H-M failure envelope decreases with the increase of the vertical load; there is a strong interaction between vertical and horizontal loads, i.e., the V-H yield surface formed by vertical and horizontal bearing capacity is approximately a quarter ellipse. It can be seen that the size of the H-M inclined ellipse is controlled by the vertical load. Based on all these results of numerical simulations, a new analytical expression is finally proposed to represent the three-dimensional failure envelope of the suction bucket foundation in V-H-M space.