•Fracture behavior of auxetic cellular structures is investigated.•A ductile damage computational modeling technique is presented.•Identification of ductile damage material parameters is given.•The influence is evaluated of the shape of unit cells on fracture behavior.•Experimental testing is carried out to validate the numerical results. Auxetic cellular structures are advanced materials with negative Poisson’s ratios, which exhibit some unique features which are useful for various applications. The objective of this paper is the numerical simulation and experimental analysis of evolution propagation under quasi-static loading conditions in selected auxetic cellular structures with different geometries and orientations of unit cells that is: (i) honeycomb structure, (ii) re-entrant structure, and (iii) rotated re-entrant structure. The failure modeling capability of Simulia Abaqus code for ductile materials is used for the numerical simulation. The paper presents in detail the calculation methodology for determination of ductile damage material parameters that, are used for further numerical simulations of the damage initiation and evolution. Standard Compact Tension (CT) specimens are selected for the numerical simulation and experimental testing. Here, the specimens are made from 7075-T651 aluminum plate, cut using water jet cutting technology. Using a numerical approach, the fracture behavior of the selected auxetic structures is estimated first. Experimental testing is also carried out to validate the numerical results. The comparison between computational and experimental results regarding crack propagation path and force-displacement diagrams showed a reasonable agreement.