This study reviewed types and dynamic behavior characteristics of shock-absorbing materials used in spent nuclear fuel transport containers. Among various shock-absorbing materials, wood, honeycomb, and foam materials were the most commonly used. Redwood and balsa wood are sustainable materials with excellent energy absorption properties and natural decomposition, but vulnerable to temperature and humidity. Although honeycomb materials have better mechanical strength than other materials, they only support unidirectional loads. Urethane foam and Fenosol foam materials have lower mechanical strength and lower shock absorption than others, but have higher lightness and fire resistance. They also allow users to control density and produce them. Due to their isotropic characteristics and ease of increasing or decreasing strength by adjusting density, foam materials are better for design and manufacturability than others. Shock-absorbing materials show more complex behavior characteristics than general steel materials. For shock absorption, large deformations are considered up to sections that greatly exceed the elastic region, inevitably increasing the complexity of behavior simulation. During design, to accurately simulate large deformation behavior, it is important to select an appropriate analysis property card and determine major influencing factors. An analysis-based review was additionally conducted for property cards typically applied to foam materials.