The use of composite sandwich plates in aerospace, marine, and lightweight civil engineering structures has become common practice as these materials exhibit favorable stiffness-to-mass ratios and excellent energy absorption capabilities. Nevertheless, there exists a lack of understanding of their non-linear behavior in the context of Low Velocity Impact (LVI) loads, especially concerning the effects of physical and geometrical characteristics on impact performance. In the current research, a new fully three-dimensional non-linear finite element formulation for the analysis of LVIs of sandwich plates, consisting of composite face sheets and flexible foam cores, is introduced using the ABAQUS platform. Contrary to the plate theory-based conventional approach, the proposed formulation uses three-dimensional elasticity theory. The influence of different physical and geometrical parameters on LVI resistance is investigated. The numerical analysis shows that a decrease in the stiffness of the composite face sheets or foam core causes a reduction in contact force and absorbed energy, while increasing local deformation and time of impact occurs. Moreover, an alteration of impactor shape from spherical to cylindrical shape enhances the contact stiffness and causes an increase in peak impact force greater than 100% at the expense of displacement and impact time reduction. It is also found that thinning of core thickness lowers bending stiffness of the sandwich panel, which results in a significant increase in impact force and deflection. The findings presented here could be useful in designing impact-resistance sandwich structures and also could be used as a basis for further theoretical and experimental researches.