An analytical model for the compressive and shear response of monolithic and hierarchical corrugated composite cores has been developed. The stiffness model considers the contribution in stiffness from the bending- and the shear deformations of the core members in addition to the stretching deformation. The strength model is based on the normal stress and shear stress distribution over each core member when subjected to a shear or compressive load condition. The strength model also accounts for initial imperfections. In part 1 of this series, the analytical model is described and the results are compared to finite element predictions. In part 2, the analytical model is compared to experimental results and the behaviour of the corrugated structures is investigated more thoroughly using failure mechanism maps.