<p>Axially moving devices are widely used in daily life, with the beam model being the most commonly used for analysis simplification. However, the inevitable transverse vibration phenomenon severely affects the stability and safety of the system. In certain devices, periodic velocity fluctuation may be observed, leading to parametric resonance. Furthermore, although the boundary conditions have an important influence, it is generally reduced to fixed or simply supported. However, such clear distinctions cannot be easily made in actual. Thus, this paper aims to analyze the principal and summation parametric resonance of a traveling beam considering boundary torsional stiffness, caused by varying velocity and tension. Natural frequencies and modes of the beam are derived based on complex modal method and validated using the differential quadrature element method (DQEM). Effects of boundary torsional stiffnesses and the variable velocity on natural frequencies of the traveling beam are discussed. To analyze the mechanism of steady-state amplitudes for both principal and summation parametric resonances, the method of multiple scales (MMS) is employed to perturb the nonlinear model. This allows for obtaining the linear homogeneous models with the modal revision method (MRM) at each time scale. Stability boundaries and its amplitude-frequency responses for principal and summation parametric resonances are derived. Furthermore, the analytical results are compared with the numerical results via the DQEM, verifying the feasibility and precision of MMS. Finally, a parametric study is performed to show the influence of some parameters on the stability boundaries of the beam and its amplitudes of different modes.</p>