This paper presents a non-parametric shape design methodology of energy absorbing panels under cyclic load with the elastic-plastic behavior The Green-Lagrange strain, the 2nd Piola-Kirchhoff stress and the stiffness tensor are employed to express the elastic-plastic problem involving material and geometric nonlinearity in finite element method The optimal shape of the panel is determined by applying the sensitivity as the fictitious external forces to the design boundaries to change the shape, while maximizing the energy absorption A calculated result is demonstrated to show the effectiveness of the convenient methodology