The paper proposes first to study the behavior of honeycomb alone under uniform cyclic compression-relaxation loading. It is found that the behavior is linear until it reaches the maximum force following by a sudden drop of force and at the end following by a constant force during the compression. This force-displacement behavior is observed to be similar for all material of honeycomb such as; Nomex (with different densities and cell dimensions), fiber-glass and aluminum. From experimental study, the behavior becomes significantly non-linear in the area of constant force (flat zone) especially the spring-back behavior. A mathematical model is proposed to simulate completely compression-spring-back behavior of honeycomb. This mathematical model describes the behavior of honeycomb in compression and spring-back loading only in function of the maximum depth due to impact. The proposed mathematical model is then integrated to FEA model to simulate the spring-back behavior of sandwich structure with metallic skins and honeycomb core. After integrating the influence of skin-honeycomb interaction, a complete mathematical model which includes non-linearity of compression-spring-back behavior and rotation due to skin-honeycomb interaction is proposed to simulate the behavior of sandwich structure subjected to low energy/ low velocity impact (indentation) loading using spherical impactor. Some simulations of indentation and relaxation on sandwich structure with nomex honeycomb using different diameters of spherical indenter and different thickness of metallic skin are obtained with a good comparison with experimental results.