<p>Uncertain parameters are widespread in engineering systems. This study investigates the modal analysis of a fluid-conveying pipe subjected to elastic supports with unknown-but-bound parameters. The governing equation for the elastically supported fluid-conveying pipe is transformed into ordinary differential equations using the Galerkin truncation method. The Chebyshev interval approach, integrated with the assumed mode method is then used to investigate the effects of uncertainties of support stiffness, fluid speed, and pipe length on the natural frequencies and mode shapes of the pipe. Additionally, both symmetrical and asymmetrical support stiffnesses are discussed. The accuracy and effectiveness of the Chebyshev interval approach are verified through comparison with the Monte Carlo method. The results reveal that, for the same deviation coefficient, uncertainties in symmetrical support stiffness have a greater impact on the first four natural frequencies than those of the asymmetrical one. There may be significant differences in the sensitivity of natural frequencies and mode shapes of the same order to uncertain parameters. Notably, mode shapes susceptible to uncertain parameters exhibit wider fluctuation intervals near the elastic supports, requiring more attention.</p>