In this study, based on continuum mechanics, an Euler–Bernoulli model has been applied to analyze the free transverse vibration of fluid conveying Single-Walled Carbon Nanotubes (SWCNTs), embedded in two-parameter elastic mediums such as; the Pasternak and viscoelastic mediums. By exerting the transfer matrix method (TMM), the vibration analysis of a fluid conveying SWCNT is developed. The effects of fluid flow velocity, Winkler, visco and Pasternak- elastic mediums are studied on the resonance frequencies. The results indicate that, the resonant frequencies at which the structural instability of nanotubes emerge are significantly influenced by their surrounding elastic medium. Each elastic medium is found to have special characteristics, resulting in different frequency behaviors for each SWCNT. Finally, the effects of geometry are studied on the SWCNT\\\\\\\'s resonance frequencies. Interesting results are obtained, which are helpful in the modeling or designing process of a carbon nanotube.

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