In the present work, the damping characteristics of clamped–clamped viscoelastic sandwich tube conveying fluid are investigated in relation to the length-to-radius and radius-to-thickness ratios. It is observed that the modal loss factor is very less for lower circumferential modes compared to higher modes while the modal loss factors of higher modes increases with the aforesaid ratios. A significant effect of flow velocity in reducing the natural frequency and enhancing the loss factor appears only in sandwich shells, whereas this effect is negligible for sandwich pipes and have very low fundamental modal loss factor. The symmetric sandwich tube conveying fluid has a better damping capability compared to an asymmetric one.