In this study, the forced vibration of cylinders reinforced by carbon nanotubes (CNTs) under a moving load is estimated based on the theory of oscillations. The composite cylinders reinforced with CNTs of infinite length subjected to combined action of the internal pressure and ring-shaped compressive pressure with constant velocity. Here, we consider uniform and nonuniform reinforcement distributions, with the mechanical properties varying linearly throughout the thickness and the effective material properties are estimated by employing the extended rule of mixture. Following the formulation of the problem, the basic equations are derived and then solved in order to determine the maximum static and dynamic deflections, dynamic factors, and critical velocity of composite cylinders reinforced with CNTs. After checking the reliability of the proposed formulation and the accuracy of the results in accordance with the available literature, a systematic study is aimed at checking the sensitivity of the dynamic response to the geometry, velocity, type of distribution, and volume fraction of CNTs.