Abstract —Crashworthiness studies involve computational analyses of complex structures. If the randomncss of the structural properties is neglected, however, the results of the analysis turn out not to be in agreement with the ones of laboratory tests. The paper systematizes a probabilistic approach to this problem which uses a response surface approximation in terms of spatial averages of the design variables. It includes the randomness of variables, vectors, and fields; it is shown to be efficient and accurate. The method requires an accurate design of the experiments to be carried out in order to identify the response surface parameters. The correlation between response variables is also analysed. A numerical example is presented. The derived results are validated by simulation.