Current design practice of spudcans in clay generally ignores the influence of installation and subsequent operation on the spudcan elastic stiffness. In reality, soil consolidation around the post-installation spudcan can cause the elastic stiffness to evolve with time, thus affecting the safe and stable operation of jack-up platforms. This paper reports a numerical study dedicated to this specific subject. The spudcan installation and the time evolution of elastic stiffness coefficients during operation are continuously simulated using an effective stress large deformation finite element technique. The effects of soil, loading, embedment and geometric conditions were evaluated and interpreted. It was found that the non-uniform growth of the shear modulus caused by soil consolidation during operation results in the time evolution of the elastic stiffness and makes the deformation mechanism asymmetric. The overlap degree between the involved zone of the deformation mechanism and the growth zone of the shear modulus (or the so-called averaging effect) affects the gradient of time evolution. Based on the parametric study, a generalized framework is present for predicting the elastic stiffness coefficients of spudcans for different scenarios and consolidation times, thus providing a complete view of the time evolution of elastic stiffness for the offshore in-site assessment.