Abstract: This paper investigates the effects of parameter uncertainties on the natural characteristics of a fluid-conveying pipe system with a single clamp constraint. Based on the generalized Hamilton principle, the dynamic equations and boundary conditions of a fluid-conveying pipe clamped at both ends and constrained by a single clamp are derived. To better reflect the parameter uncertainties commonly presented in engineering practice, the dynamic equations with interval uncertainties are established by the interval analysis theory. The upper and lower bounds of the natural frequency intervals of the single-clamped fluid-conveying pipe considering uncertain parameters are obtained using the uncertain analysis method based on the Lagrange surrogate model. The accuracy of the proposed method is verified by comparison with results obtained from the scanning method. The effects of uncertainties in parameters such as the clamp position, fluid speed, linear stiffness, and torsional stiffness of the clamp on the natural frequencies of the pipe system are discussed in detail. The results show that with increasing coefficient of variation of the uncertain parameters, the intervals of the first four natural frequencies become wider, with the clamp position having the significant effect. For different clamp positions, when the median value of the uncertain clamp position is located at 0.5 m and 0.3 m along the pipe, the upper and lower bounds of the first four natural frequency intervals exhibit non-monotonic and nonlinear variation as the coefficient of variation increases. In contrast, when the median value is located at 0.1 m, the intervals of the first four natural frequencies exhibit monotonic and linear variation.