<p>Composite materials present several applications in different types of mechanical components and structures due to their wide range of advantages, such as high stiffness and resistance as compared to their weight and their ability to change stiffness and damping characteristics through the manipulation of their properties. In this way, researchers in the field of rotor dynamics have seen the use of these materials instead of metallic ones as an opportunity to maximize operating speeds, reduce the time of acceleration and deceleration, increase structural efficiency, among other aspects. In the present contribution, a finite element model of a composite material hollow shaft was formulated by considering the Kelvin–Voigt rheological model and the simplified homogenized beam theory to obtain the properties of the composite material shaft, from which internal damping and stiffness matrix are determined. The dynamic behavior of the system is influenced by internal damping and stiffness matrix. Therefore, interval uncertainty and sensitivity analyses were applied to a composite material shaft under two different sets of boundary conditions, namely free–free condition and the shaft assembled as a component of an experimental rotor-bearing system. The main scientific contribution of this work lies in the comprehensive evaluation of the composite material hollow shaft’s frequency response functions by considering a more extensive set of uncertain parameters as compared to previous studies. Moreover, the present work introduces a dedicated analysis of the effects of rotation speed on the shaft’s dynamic behavior, which was not addressed in earlier contributions. The obtained results demonstrated that the most important parameters for changing the vibration responses of the shaft depend on the excitation frequency (rotor at rest) and rotation speed (rotating machine).</p>