The book describes the theoretical model of an energy-absorptive bumper which protects vehicles from a crash. The first part describes the question of passive safety as well as the classification, criteria of quality and the state of researches. In the next chapters the book presents the worked out method of projecting the layered bumper with the original construction (2 patents) and the method of analysis of the processes of absorption a crash energy by it in the four stage process. The book describes: the study of conception of the bumper construction, execution the experimental researches with bumper elements and the model of the bumper, study of the algorithm of projecting as well as the execution the numeric 2D simulation of FEM of absorption by bumper the energy in the linear range with buckling and non-linear. Is also presented the dynamic analysis of work of bumper, i.e. the differential equations for every stage of the energy consuming process and the calculation for the bumper.