An effective single layered finite element (FE) computational model is proposed to predict the structural behavior of lightweight sandwich panels having two dimensional (2D) prismatic or three dimensional (3D) truss cores. Three different types of cellular core topology are considered: pyramidal truss core (3D), Kagome truss core (3D) and corrugated core (2D), representing three kinds of material anisotropy: orthotropic, monoclinic and general anisotropic. A homogenization technique is developed to obtain the homogenized macroscopic stiffness properties of the cellular core. In comparison with the results obtained by using detailed FE model, the single layered computational model can give acceptable predictions for both the static and dynamic The project supported by the National behaviors of orthotropic truss core sandwich panels. However, for non-orthotropic 3D truss cores, the predictions are not so well. For both static and dynamic behaviors of a 2D corrugated core sandwich panel, the predictions derived by the single layered computational model is generally acceptable when the size of the unit cell varies within a certain range, with the predictions for moderately strong or strong corrugated cores more accurate than those for weak cores.