Military ships carry sensitive articles and equipment that experience shock loads caused by underwater explosions in the vicinity of the ship. Unwanted shock loads of this kind have the potential to damage extremely energetic objects and compromise the accuracy of extremely delicate machinery. This research aims to perform a finite element (FE) analysis of ring-shaped hydrogenated nitrile butadiene rubber (HNBR) and Sorbothane isolators to protect a sensitive article stored inside a cylindrical-shaped component of a naval ship using ABAQUS. These materials have nonlinear elastic and viscous properties, which are modeled in the ship component’s FE model by the third-order Ogden and generalized Maxwell models, respectively. The material constants of these models are determined using the experimental test data of HNBR and Sorbothane. A transverse shock with a peak amplitude of 60 g is applied at the outer surface of the component, and responses are measured in the form of acceleration of the article, deformation, and stress distribution in the isolators. The proposed HNBR and Sorbothane isolators of considered length provide 97.16% and 98.23% shock reduction with 15.23 mm and 9.5 mm maximum deflection in the isolators, respectively. Moreover, the maximum stress developed in the isolators is within the tensile strength of the materials.