AbstractPreviously, a sandwich structure in which the Poisson ratios of the core and facesheets possess opposite signs has been shown to exhibit overall conventional and auxetic behavior depending on the loading mode – axial loading or bending – for an intermediate range of relative core thickness. In addition to these two loading modes, sandwich structures in aerospace applications encounter torsional loads. In this paper, the effective Poisson's ratio for torsional loading is proposed. Results show that, depending on the loading mode and the relative core thickness, there can be up to four levels of overall auxeticity, namely (i) full auxeticity (FA) if the structure behaves as an auxetic structure under all three modes of loading, (ii) high auxeticity (HA) if the structure behaves as an auxetic structure in two of the loading modes, (iii) low auxeticity (LA) if the structure behaves as an auxetic structure in only one of the loading modes, and (iv) no auxeticity (NA) if the structure behaves as a conventional structure under all of the three loading modes. These results indicate that by selecting the Poisson's ratios and the thickness of the cores and facesheets, the sandwich structure can be made to respond differently under different external loading conditions.