The elastic stiffness of spudcan foundations in stiff-over-soft clays exhibits changes similar to “punch-through” failure, creating significant uncertainty for jack-up platform operations. This study conducted a three-dimensional small-strain finite element analysis on this specific topic to discretely simulate the spudcan elastic stiffness profile in stiff-over-soft clay. The influence of the soil surface, layered interface, and their coupling effects were isolated and separately evaluated, and a simple semi-theoretical framework for the influence zone was proposed. The key parameters of layered soil (thickness ratio, shear modulus ratio, soil heterogeneity coefficient, and backflow) affecting the influence mechanism of spudcan elastic stiffness were evaluated and analyzed. It was found that the effects of the soil surface and layered interface competed with each other. The vertical deformation mechanism of the spudcan reduces the “punch-through” failure risk of elastic stiffness by transferring more of the soil deformation to the bottom soft clay layer. Based on the findings from the parameter study, a simplified profile is proposed to predict the variation of the spudcan elastic stiffness. The proposed prediction method provides a comprehensive view of elastic stiffness in stiff-over-soft clay for offshore in-site assessment.