Based on three-dimensional large deformation finite element method utilizing coupled Eulerian-Lagrangian algorithm, the penetration responses of square spudcan in strong over soft clays were numerically simulated. The effects on the penetration resistance curve were studied of the strength ratio of the bottom clay layer to the top clay layer, the relative thickness of the top layer, the unit weight of soil, and the coefficient of earth pressure at rest. The soil deformation mechanism of punch-through failure during penetration was investigated. The results show that the strength ratio of the bottom clay layer to the top clay layer and the relative thickness of the top layer significantly affects the penetration resistance of square spudcan footings. The peak bearing capacity factor of square spudcan decreases somewhat with the decrease of the coefficient of earth pressure at rest. The penetration resistance curve does not obey the available equation proposed by other authors due to the possible difference of unit weight of the top layer and the bottom layer. The square spudcan footings experience punch-through failure when the proposed dimensional parameter in terms of footing width, the unit weight and undrained strength of upper soil is less than a critical value in the condition that the thickness of upper clay layer is defined and the difference of unit weight of the layers is not appreciable.