<p>Pipes have been extensively utilized in the aerospace, maritime, and other engineering sectors. However, the vibrations of pipes can significantly affect the system reliability and even lead to accidents. Visco-hyperelastic materials can enhance the dissipative effect, and reduce the vibrations of pipes. However, the mechanism based on the constitutive model for visco-hyperelastic materials is not clear. In this study, the damping effect of a visco-hyperelastic material on the outer surface of a plain steel pipe is investigated. The nonlinear constitutive relation of the visco-hyperelastic material is introduced into the governing equation of the system for the first time. Based on this nonlinear constitutive model, the governing model for the forced vibration analysis of a simply-supported laminated pipe is established. The Galerkin method is used to analyze the effects of the visco-hyperelastic parameters and structural parameters on the natural characteristics of the fluid-conveying pipes. Subsequently, the harmonic balance method (HBM) is used to investigate the forced vibration responses of the pipe. Finally, the differential quadrature element method (DQEM) is used to validate these results. The findings demonstrate that, while the visco-hyperelastic material has a minimal effect on the natural characteristics, it effectively dampens the vibrations in the pipe. This research provides a theoretical foundation for applying vibration damping materials in pipe vibration control.</p>