Under quasi-static uniaxial compression, inserting aluminum foams into the interstices of a metallic sandwich panel with corrugated core increased significantly both its peak crushing strength and energy absorption per unit mass. This beneficial effect diminished however if the foam relative density was relatively low or the compression velocity became sufficiently high. To provide insight into the varying role of aluminum foam filler with increasing compression velocity, the crushing response and collapse modes of all metallic corrugate-cored sandwich panels filled with close-celled aluminum foams were studied using the method of finite elements (FEs). The constraint that sandwich panels with and without foam filling had the same total weight was enforced. The effects of plastic hardening and strain rate sensitivity of the strut material as well as foam/strut interfacial debonding were quantified. Three collapse modes (quasi-static, transition, and shock modes) were identified, corresponding to different ranges of compression velocity. Strengthening due to foam insertion and inertial stabilization both acted to provide support for the struts against buckling. At relatively low compression velocities, the struts were mainly strengthened by the surrounding foam; at high compression velocities, inertia stabilization played a more dominant role than foam filling.