A comprehensive theoretical and experimental study is presented of the bandgap behavior of periodic viscoelastic material (VEM) composites subjected to impact loading. The composites under consideration consist of an assembly of aluminum sections integrated with periodic inserts which are arranged in one-dimensional configurations. The investigated inserts are manufactured either from VEM only or VEM with local resonators (LR). A finite element model (FEM) is developed to predict the dynamics of this class of VEM composites by integrating the dynamics of the solid aluminum sections with those of VEM using the Golla-Hughes-Mctavish (GHM) mini-oscillator approach. The integrated model enables, for the first time, the accurate predictions of the bandgap characteristics of periodic viscoelastic composites unlike previous studies where the viscoelastic damping is modeled using the complex modulus approach with storage modulus and loss factor are assumed constants and independent of the frequency or the unrealistic and physically inaccurate Kelvin–Voigt viscous-damping models. The predictions of the developed FEM are validated against the predictions of the commercial finite element package ansys. Furthermore, the FEM predictions are checked experimentally using prototypes of the VEM composites with VEM and VEM/LR inserts. Comparisons are also established against the behavior of plain aluminum rods in an attempt to demonstrate the effectiveness of the proposed class of composites in mitigation of the structural response under impact loading. Close agreements are demonstrated between the theoretical predictions and the obtained experimental results.