In order to describe the different types of uncertainty parameters for the thickness and material parameters of absorbing energy structure, probability and convex set models were adopted. The reliability indices for vehicle frontal impact safety were chosen as the reliability constraints and the weight of absorbing energy structure was selected as the objective of optimization. Then, an optimization design of structures subjected to vehicle frontal impact was formulated. The Kriging models for obiective and constraint functions were constructed by using the method of Latin hypercube experiment...