Uncertain structural parameters increase the mechanical failure risk of the drilling riser system. The effect of uncertain structural parameters on the mechanical characteristics of the drilling riser system is unclear. Therefore, the mechanical characteristics of the drilling riser system with structural parameter uncertainty are analyzed. A mechanical model with uncertain structural parameters is established based on the basic analysis model and the local average theory. The basic analysis model takes into account the combined effects of platform motion, tensioner, riser string, and marine environment. The local average theory is suitable for situations where there is a lack of uncertainty information. A solution approach is proposed using the second-order central perturbation method and the Newmark-β method. The solution method reduces the load by simplifying degrees of freedom and random variables. The correctness of the solution method is verified using the Monte Carlo method. The analysis results indicate that uncertain structural parameters significantly affect the static response, while the dynamic response is less affected. The failure risk due to static axial stress and static shear stress is heightened by uncertain structural parameters. The failure risk arising from static shear stress at the bottom of the riser system experiences a significant increase.