In this paper, a new type of filled doubly re-entrant auxetic lattice structure for application in damping and energy absorption devices is considered. The structure is modeled to give protection for machines and mechanisms of intensive impact. The suggested structure is the modified version of the auxetic one with silicone fillings. The unit of the structure is assumed as a re-entrant hexagon with four quadrangular absorbers. For the assumed model of unit, the deformation properties and the Poisson’s ratio were computed. The obtained results were experimentally tested. Specimens of filled and unfilled structures were investigated under quasi-static compression. The measured results show that the energy dissipation is more than two times higher for filled structure than for unfilled ones. In the filled structure, the absorber’s rigidity has the crucial role. If the rigidity is small, the absorber, inside the unit, continues to deform from rectangle into rhomboid. Otherwise, if the rigidity is high, units with absorbers form a beam-like structure that buckles and shows high energy absorption effect. The experimentally obtained results are in good agreement with the theoretical ones.