Thermoplastic polyester elastomer (TPEE) possesses the properties of both rubber and engineering plastic. The most important feature of this material lies in its ability to combine the superior repulsion elasticity and flexibility of rubber with the rigidity of engineering plastic. This enables it to exhibit durability against fatigue, even when exposed repeatedly to large deformation.The most remarkable feature of TPEE is such that it can realize material properties with very small strain rate dependency. The authors have had their ample experiences with applying TPEE to large damper members in the civil engineering structures, such as fenders surrounding the piers of bridges to absorb the impact energy caused by ship collisions and the aseismatic connectors built in bridge structures. This paper attempts to develop shock absorbing components of small sizes with light weight for automobile applications. Locating TPEE shock absorbers inside the crash box (members connecting the bumper system to the main body) may be thought as a typical application of the TPEE products.In order to achieve weight saving of the shock absorbing components, it is effective to utilize the buckling behaviors of thin walled structures. With regard to the buckling simulations of cylindrical shell structures, the authors have been working to develop analysis procedures for obtaining stable solutions utilizing the latest general-purpose finite element technology.This report shows that the experimental results could successfully be reproduced by applying the simulation technique to the honeycomb-shaped shock absorbing components. For realizing a desirable load-displacement relationship, this report also shows how to modify the shape of the components.