In this paper, we aim to reveal the influence of fault fracture zones on the stability of submarine tunnels and the surrounding rock under different water and drainage measures. Firstly, four typical working conditions of submarine tunnels intersecting with fault fracture zones were selected. On the basis of the typical cross section of the intersections of submarine tunnels and faults, they were divided into four working conditions. Then, the displacement and plastic zones of the surrounding rock of the tunnel were studied, and the stability of the rock surrounding the submarine tunnel was discussed. This research structure indicates that the bending moment and axial force of the lining structure of the submarine tunnel increase with increasing sealing degree, but the safety factor exhibits a downward trend. When the fault fracture zone goes through the section above the tunnel axis, the bending moment and axial force at the lining vault are greater than the other working conditions, and the displacement of the surrounding rock at the vault and spandrel is prominent. When the fault fracture zone completely passes through the tunnel, the safety factor of the lining structure is at its lowest, and the displacement of the surrounding rock at the arch waist develops laterally. When the fault fracture zone passes through the part below the tunnel axis, the arch foot displacement converges significantly, and the surrounding rock displacement exhibits a downward inclination. In addition, the plastic zone is mainly developed in the arch and the shoulder. These research results provide a reliable reference for tunnel design and excavation support.