This work aims to develop a size-dependent mathematical model to analyze the nonclassical sizedependent vibration response of viscoelastic perforated higher-order nanobeams (VEPHONBs) embedded in an elastic foundation and subjected to dynamic moving loads. The nonclassical strain gradient theory is adopted to capture the microstructure as well as the size length-scales effects. The Kelvin–Voigt viscoelastic material model is utilized to simulate the internal material damping. Regular square perforation pattern is considered. Shear deformation effect due to cutouts is incorporated by adopting the higher-order shear deformation beam theory. The moving load is portrayed by point load and harmonic type. The Hamilton approach is applied to derive the dynamic equations of motion considering viscoelasticity as well as size dependency effects. Based on the Navier and Newmark techniques, a mixed analytical–numerical solution is developed and verified by comparing the obtained results with the available results in the literature. Parametric studies are conducted to show the influence of the different design parameters on the transient vibration behavior of viscoelastic perforated higher-order nanobeams under moving load. The proposed procedure is supportive in the analysis and design of perforated viscoelastic NEMS structures under moving load. 1 Introducti