The effects of important physical and geometrical parameters on transverse low-velocity impact response of composite sandwich panels have been studied in this paper. Impacts are assumed to occur normally over the top and/or the bottom face sheets, at arbitrary locations and with different impactor masses and initial velocities. For deriving closed-form solutions for the contact force, displacements of the impactor and the panel in the transverse direction, the sandwich panel has been modeled as a discrete three-degrees-of-freedom dynamic system with equivalent masses and springs (SM). The dynamic response of the panel is based on the improved higher-order sandwich plate theory (IHSAPT) and both thick and thin panels have been analyzed. The effects of transverse flexibility of the core, and boundary conditions are considered. Also, the area of the contact patch between the impactor and the panel can be varied as it changes with contact duration. The numerical results of the analysis have been compared either with the available experimental results or with some theoretical results. It is established that the dynamic behavior of the sandwich panel depends on various parameters, such as the aspect ratio and the length-to-thickness ratio of the panel, core thickness, boundary conditions of the panel and impactor parameters like its potential energy, velocity and the location of contact point, etc.