Using the press-replace technique, a recently developed finite element method depending on the criteria of the small deformation analysis SDA, to investigate the soil-foundation interaction of the Jack-Up rig with Spudcan during its proceeding to achieve stability installation in Multi-Layered soil. The analysis has been implemented and compared with previously published cases, which has been done experimentally and by using large deformation finite element analysis. The Press-Replace technique PRT is mainly has been developed able to capture the Spudcan proceeding through the multi-layered soil specifically in cases of penetrating through soft soils by simulating the possible squeezing accompanied by the back-flow phenomenon, which happens for the soft soil during the installation. The considered analysis criteria have been explicated. The results provided an effective expectation of the soil-structure interaction validated by the previous experimental and numerical results. Depending on the detailed analysis steps provided, engineers and researchers can use it to make the needed analysis for similar case studies. The small deformation analysis SDA has been operated on six cases of multi-layered soils and compared to the previous experimental and numerical results. The variety of investigated cases was depending on the type of upper layered, either it was a soft to moderate clay layer or a sand layer. The two main criteria have been considered in the current analysis, which is the backflow of clay and the back-fill of sand. As the analysis theory depends mainly on the geometry update, the simulation steps of these two criteria have been provided in detail. That control has been applied, by observing the soil movement behavior of the previous experimental outcomes. Four cases with upper clay soil and other two cases with upper sand layers have been investigated and compared to previous experimental and numerical results. By controlling these two states of the upper soil layer, it can be obtained the different simulation steps in the analysis in the condition of the existing upper layer is sand or clay. The analysis provided shows a good comparison of stability depth to the previous results. Furthermore, it gives a very close evaluation behavior to the previous experimental results. This approach numerical method provides a tool for the engineers to use the Press-Replace technique PRT, which is a smooth and fast numerical technique compared to the other numerical methods, to investigate and obtain the Spudcan penetration through similar cases of multi-layered soil.