To investigate the flexible support of the incompressible seal, negative stiffness characteristic was analyzed. The rotor dynamic coefficients in the neck bush and the ring seal in the LNG pump were predicted by employing three-dimensional flow model, the κ-ε turbulence model and numerically solving the Navier-Stokes equations. The dynamic characteristics were compared in the incompressible seals over a range of rotating speeds and between nominal clearance and twice clearance seals. Through simulating the incompressible flow, as well as analyzing and comparing the circumferential distributions of the pressure and velocity, the reasons for the negative direct stiffness in the uniform annular seal were discovered and the influences on the negative direct stiffness were also found. The results show that: for both the annular seal and the grooved seal, the direct stiffness of twice clearance seal was higher than that of the normal clearance seal, but the cross stiffness of twice clearance seal was smaller than that of the normal clearance seal. It indicated the rotor stability was improved after seal wore. The direct stiffness dropped and the cross stiffness increased with the increase of the rotating speed, which caused rotor stability reduction. In the high rotating speed condition, the annular seal with a small clearance was vulnerable to perform a characteristic of negative stiffness, which destroyed the stability of the rotor system. It is recommended that the grooved seals are applied to the pump to control the incompressible flow against leakage instead of the annular seal.