In the context of nonclassical continuum mechanics, the nonlocal strain gradient theory is employed to develop a nonclassical size dependent model to investigate the dynamic behavior of a CNTs reinforced composite beam resting on two parameters elastic foundations under a moving load. The governing dynamic equations of motion are derived based on thirdorder shear deformation theory using Hamilton’s principle. An analytical solution methodology is developed using Navier’s procedure is developed to derive the analytical solution for the equations of motion. The developed methodology is checked and compared. Parametric studies are conducted to demonstrate the applicability of the developed procedure to investigate the dynamic behavior of CNTs beams under moving load. Effects of the elastic foundation parameters, volume fraction, CNTs configuration, the nonclassical parameters, and the moving load velocity parameter on the dynamic behavior of CNTs beams under moving load are investigated and analyzed. The obtained results are supportive for design and manufacturing of composite CNTs beams.