Traditional sandwich structure consists of two face sheets and a core. With an internal sheet inserted into the core, a two-core sandwich structure is then formed. Two-core sandwich structures with composite laminated face sheets and a thin internal sheet subjected to low velocity impact are studied in this paper. Local displacement of the core under the point of impact is investigated. Simulated results show that the local displacement of the core along the direction of the impact has been decreased significantly by introducing the internal sheet into a traditional single sandwich structure and by reducing the space between the internal sheet and the impacted face sheet. Shear deformation in the cores of a two-core sandwich structure is also investigated and attention is focused on shear strains on interfaces between face/internal sheets and the cores. Results further show that strain levels in selected elements at the interested interfaces depend upon locations of the selected elements and arrangements of the internal sheet.