The development of sustainable sandwich materials is needed in the transportation sector to address environmental concerns related to the production and operation of vehicles. In addition to biobased composite skins, alternatives to classic synthetic core materials must be found to reduce the ecological footprint of whole sandwich-structured composites. This study focused on three eco-friendly lightweight core materials: balsa wood, paper honeycomb, and recycled PET foam. The effect of the hygrothermal ageing on their shear creep/recovery behaviour has been here investigated. Two different environmental conditions were tested: 23 °C-50% RH and 70 °C-65% RH. The results indicate that the maximum shear strain , the time-delayed strain and the residual strain increase for the three core materials with the severity of the hygrothermal conditions. This was attributed to the softening of the constitutive polymeric materials of the cell walls at temperatures close to 70 °C. The balsa wood exhibits the best creep resistance under the two environmental conditions. The identification of the viscoelastic properties highlights that the release times and the shear viscous parameters of the balsa wood and the PET foam depend on the stress level and the hygrothermal conditions.