One of the most important factors in the process of jack-up rig installation is the good expectation of the amount of spud-can penetration into soil layers under the varying loads. It is important to insert the spud-can through soil layers up to the expected stability depth during the installation process to guarantee enough soil stability reaction. The Press-Replace Technique (PRT), which is considered a kind of small-deformation nonlinear-material finite-element analysis, is applied in this paper to track the full load-penetration response of a spud-can in double-layered soil. A parametric study was carried out by using Plaxis 2D Vr.8.6 to evaluate the effect of the strength properties of soil on the Punch-through phenomenon and the bearing capacity of soil spud-can system by applying the Press Replace Technique (PRT). This study is also concerned with the penetration of a circular spud-can in stiff clay over either soft clay or loose sand soil. Among the considered properties of the soil, it was demonstrated that the undrained shear strength of top stiff clay layer is the most important parameter that affects the penetration response of spud-can in this case, where the properties of the lower soft clay layer do not have major effect.