On the basis of the composition of organs and static theory, a bionic periodic isolation structure is modeled to study the mechanical characteristics of vibration isolation with the aim of isolating ship vibration. The unit cell of the structure is composed of three layers, an upper steel layer, a middle stiff rubber layer, and a bottom soft rubber layer, and some multicell units are analyzed. To maintain numerical accuracy, the mapping method is used to mesh the periodic model with an element size of 0.01 mm. In the case of a static load, all the unit cells exhibit bulging deformation on two sides. The maximum deformation is not always at the upper layer, with the maximum bulging at two sides in the single-cell case and deformation in the middle layer in the cases of 9 and 10 cells. When the number of cells is above 6, deformation is enhanced in the middle layer, with half a sinusoidal wave. In this paper, the deformation ratio in the middle layer is as high as 87.99%. In addition, the stress distribution characteristic is also compared among some cases. The bionic isolation structure and its analysis may provide a new way to reduce the vibration in a ship.