Due to their ability to buffer and attenuate vibrations, as well as their low cost, rubber-based isolators are widely used in military and civilian vessels. Since these isolators are part of a ship’s structure, the accurate prediction of their static and dynamic performance is essential for overall structural design. In this paper, two kinds of marine shear-compression rubber isolators of different models in the same series are taken as the research objects, and the static and dynamic constitutive models of the rubber materials are obtained through material tests, which are used as inputs to accurately predict the static and dynamic characteristics of the isolators in the three translational directions through numerical calculations. The effects of size and preload force on the dynamic characteristics of the vibration isolators were analyzed as were the reasons for the peaks in the impedance curves. The results show that the preload force increases the amplitudes of the peak transfer impedance in the X direction and decreases it in the Z direction. On the other hand, as the size of the vibration isolator increases, the peak frequency of the transfer impedance in the X direction increases, while in the Y and Z directions, the first-order peak frequency decreases and the second-order peak frequency increases. The peaks of the transfer impedance curves appear due to the resonance of the embedded metal blocks, and the order of appearance of the resonance modes is fixed.