Given the significance of energy absorption in various industries, light shock absorbers such as honeycomb structure under in-plane and out of plane loads are are receiving a great deal of attention. In this research an analytical equation for plateau stress is represented, taking power hardening model into consideration. The equation of specific absorbtion of graded honeycomb structure with the locking strain and strain energy equation is represented. The structure, made from five aluminum grades is simulated in ABAQUS/CAE for elastic-perfectly plastic and power hardening model; numerical value of absorbed energy is compared to that of analytical method. A drop weight test on a graded honeycomb structure was performed. Based on the numerical simulation results, the experimental and numerical results showed good agreement. Based on the conducted comparisons, the numerical and analytical results are more congruent for power hardening model rather than elastic-perfectly plastic one. In the first step of optimization, by applying SQP method and genetic algorithm, the ratio of structure mass to the absorbed energy is minimized. In the second step, regarding the optimum value of parameters obtained in the first step, the material property of each row is changed. According to the optimization results, while keeping the mass of structure constant, the structure capacity of absorbing energy is increased by 18% in the first step and 264% in the second model, compared to the primary model.