This study conducts numerical analyses on a newly developed double-layer steel-lightweight high ductility cement composite (LHDCC)-steel sandwich panel under concentrated punching load. Energy absorption ability serves as an important criterion in evaluating the performance of the protective sandwich structures. One critical factor related to energy absorption ability is the stiffness or the deformation capacity of the structure. The present study first develops a procedure to establish a FE model of the double-layer SCS panel. The Concrete Damage Plasticity (CDP) model is adopted to simulate the behavior of LHDCC, with a compressive stress–strain relation represented by a statistically stochastic damage constitutive model. The FE model is validated through comparisons with the test results of 2 single-layer SCS panels and 8 double-layer SCS panels. A series of parametric studies are then performed to check the influences of concrete height, shear span, steel plate thickness, shear connector spacing, loading patch size, concrete strength and steel plate strength on the stiffness and load resistance of the panel. Finally, the paper develops a simplified analytical model to predict the stiffnesses at both elastic and plastic stages, and proposes an idealized load–displacement model to reproduce the load-deformation relation for the double-layer SCS panels. The comparisons with the test and FE results validate the accuracy of the analytical model.