This paper proposes a dynamic drop weight impact simulation to predict the impact response of 3D printed polymeric sandwich structures using an explicit finite element (FE) approach. The lattice cores of sandwich structures were based on two unit cells, a body-centred cubic (BCC) and an edge-centred cubic (ECC). The deformation and the peak acceleration, referred to as the g-max score, were calculated to quantify their shock absorption characteristic. For the FE results verification, a falling mass impact test was conducted. The FE results were in good agreement with experimental measurements. The results suggested that the strut diameter, strut length, number and orientation, and the apparent material stiffness of the lattice cores had a significant effect on their deformation behavior and shock absorption capability. In addition, the BCC lattice core with a thinner strut diameter and low structural height might lead to poor shock absorption capability caused by structure collapse and border effect, which could be improved by increasing its apparent material stiffness. This dynamic drop impact simulation process could be applied across numerous industries such as footwear, sporting goods, personal protective equipment, packaging, or biomechanical implants.