Accurate and deep understanding of the mechanical and physical behavior of sandwich panels with soft elastomeric foams, e.g. cellular solids, such as ethylene vinyl acetate is a key task in designing these structures, and also optimizing their mechanical behavior. The main objective of the present research is to present an applicable method to determine the non-linear hyper-viscoelastic response of elastomeric sandwich panels to low velocity impact loadings, by presenting an applied method. A combination of experimental results and finite element analysis, in conjunction with optimization method is used to determine the hyper-viscoelastic behavior of the studied sandwich panels. The suggested combinational approach can replace the time-consuming and expensive creep and/or relaxation experiments. A relatively simple approach is proposed to identify time-dependent viscoelastic material behavior of elastomeric foams. The calibrated finite element model is utilized to perform a set of parametric studies and the effect of various material properties is studied on the low velocity impact response of sandwich plates.