Suction bucket foundations are increasingly used in ocean engineering. The numerical analysis of the installation procedure is helpful in engineering practice. A two-dimensional axisymmetric model has been implemented into the finite element software ABAQUS based on the ALE (Arbitrary Lagrangian-Eulerian formulation) technique, which will be used to simulate the penetration process of the suction bucket foundation in clay. The undrained shear strength and elastic moduli of soil vary with the soil depth, which are considered through the subroutine VUFIELD. Centrifuge testing results and theoretical calculations are used to validate the proposed FEM model, and some key parameters including the penetration resistance, the height of soil plug under different suctions and the bucket wall friction are examined. The numerical results show that the ALE technique is capable of simulating the suction bucket penetration without mesh distortion problems. The installation method can significantly affect the penetration resistance, namely, the suction penetration can reduces the resistance significantly compared to the purely jacked penetration. In addition, it is found that as the final suction increases, the penetration resistance reduces and the soil plug height increases. It is also shown that the internal friction has a significant contribution to the penetration resistance and the properties of soil-bucket wall friction exert more significant impact on the purely jacketed penetration than on the suction penetration.