The safety and stability of the jack-up platform and jacket platform are probably threatened by the differential settlements of the spudcans in the process of translating the upper block of the offshore booster station, so it is urgent to conduct the safety and stability analysis of the relevant platform structures in this process. A 3D elastoplastic numerical calculation model is constructed using Abaqus finite element software to simulate the interaction between the upper block, either a jack-up platform or a jacket platform, and the soil foundation. The rationality and reliability of the proposed model are verified using the existing theoretical methods. The DLOAD subroutine is adopted to conduct the secondary development to simulate the complex loading situation of the platform in the process and determine the most unfavorable loading position. The safety and stability analysis of the jack-up platform and the jacket platform is conducted. The results show that the maximal longitudinal slope of the Self-Propelled Module Transporter (SPMT) unit track on the jack-up platform is only 0.69‰, which is much less than the specification requirement of 2.00%, so it is believed that the jack-up platform is able to satisfy the safety and stability requirements during the translation of the upper block of the offshore booster station. The safety factor for the pile foundation bearing capacity of the jacket platform is 1.29, which is less than the requirements in API specification. The structural safety margin of the jacket platform is insufficient, posing certain safety hazards. The research results can provide references for similar projects.