The operation of a warship is commonly affected by shock loads in different directions during sailing in a rough sea, which can decrease the precision of the shipboard equipment. To improve the shock resistance performance of the shipboard equipment, an isolator is usually installed to isolate it from the vibration of the ship deck. The paper proposes a method for dynamic response and time-variant reliability analysis of an eight-rod shock isolator (ERSI). ERSI has a novel symmetrical structure, which can improve the utilization of the isolation rods compared with the classical parallel mechanism. The isolator is modeled using Denavit-Hartenberg (D-H) convention and screw theory. Then, Duhamel integral is employed to derive the dynamic response to the isolator after decoupling the governing equation using the modal analysis method. Considering impacts of uncertain factors, this paper also presents a practical method for time-variant reliability analysis of ERSI. Finally, a discussion of the practical example of this method along with a detailed analysis to evaluate the efficiency of the proposed method is presented.