The static and low-cycle durability of three planar cellular structures, hexagonal, auxetic and auxetic-chiral, have been compared. The three structures have the same critical cross-section and are made from an aluminium alloy Al7075-T651. The reference region of each structure is represented by a matrix of nine elementary shaped cells (3 rows by 3 columns). For each structure static and low-cycle fatigue experiments at different loading amplitudes were made. Numerical simulations were then performed for the same boundary conditions to predict the static and low-cycle fatigue durability. For this purpose a continuum damage mechanics approach with element removal was used in explicit dynamic simulations. The results of static simulations were also checked using the eXtended Finite Element Method (XFEM). All the numerical simulations were carried out using Abaqus. Good agreement was observed between the simulated and measured results for each of the three cellular structures.