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Abstract Mechanical metamaterials with negative Poisson’s ratio (NPR) have emerged as a novel class of engineering material, and have attracted increasing attention in various engineering sectors. Most studies available on the buckling problem of laminated plates with positive or NPR are those under uniaxial compression. Here, we report that the buckling phenomenon may occur for auxetic nanocomposite laminated plates under uniaxial tension when the unloaded edges of the plates are immovable. Two types of nanocomposites are considered, including graphene/Cu and carbon nanotube/Cu composites. Governing equations of the auxetic nanocomposite laminated plates are formulated based on the framework of Reddy’s higher-order shear deformation theory. In modeling, the von Kármán nonlinear strain–displacement relationship, temperature-dependent material properties, thermal effects, and the plate–substrate interaction are considered. The explicit analytical solutions for postbuckling of auxetic nanocomposite laminated plates subjected to uniaxial tension are obtained for the first time by employing a two-step perturbation approach. Numerical investigations are performed for tension buckling and postbuckling behaviors of auxetic nanocomposite laminated rectangular plates with in-plane NPR rested on an elastic substrate under temperature environments.