The objective of this work is to study the large deflection of geometrically asymmetric metal foam core sandwich beam under transverse loading by a fiat punch. A yield criterion is proposed for geometrically asymmetric metal foam core sandwich structures, and then analytical solution for the large deflection of a fully clamped slender sandwich beam is obtained, in which the interaction of bending and stretching induced by large deflection is considered. Also, finite element (FE) analysis is carried out. Comparisons of the analytical solution with numerical results are presented and good agreements are found. The effects of asymmetric factor, core strength and loading punch size on the structural response of asymmetric sandwich beam are discussed in detail. It is shown that the axial stretching induced by large deflection has significant effect on the load-carrying and energy absorption capacities of geometrically asymmetric sandwich structure, but the effect of asymmetry is negligible as the deflection is larger than the depth of the sandwich beam.