This study investigated the effect of an auxetic structure, positioned as the central layer in a three-layered cylindrical shell, on its buckling behaviour. The material for all three layers is aluminium. The covers are assumed isotropic. Axial and static loads are modelled as pressure on the shell's surface. In this study, modified shear deformation theory and Galerkin's numerical solution method were used, and the effect of the presence of an auxetic core on the buckling behaviour of a three-layered cylindrical shell was investigated. The assumed structure for the auxetic cell was a 2D Re-entrant honeycomb. Finally, we explore how the length-to-radius ratio, core thickness-to-total thickness ratio, and cell angle of the auxetic structure impact the system's stability, presenting the results. The distinguishing feature of the current work compared to previous studies lies in its mathematical approach. We present the system's equations as comprehensively as possible. Finally, the effect of the length-to-radius ratio, the auxetic layer's thickness relative to the whole shell's thickness, and the cell angle's size on the buckling load were investigated. In short, with the increase of both ratios, the amount of load required for buckling decreases, or in other words, system stability is reduced. Also, the size of the cell angle has little effect on the system's stability.
