Carbon nanotubes hold substantial and exciting promise as nanocontainers filled with fluid or nanopipes conveying fluid in their hollow cavity in nanotechnology. This paper studies the coupled vibration of embedded fluid-filled multiwalled carbon nanotubes (MWNTs) subject to axial load using the multiple-Euler beam model and considering the distinctive intertube deformation of carbon MWNTs. Through the numerical examples, the effective scope of the single-beam model is examined, and the effect of the internal fluid on the coupled vibration for various geometric dimensions, mass densities of the fluid, Winkler constants, axial loads, and mode numbers, is investigated. It is found that the influence of fluid coupling effect on the natural vibrating frequencies of fluid-filled MWNTs increases as the density of the fluid increases, or as the diameter of the innermost tube increases, or as the mode number studied decreases, and, the higher mode number n or density of the fluid rho(f) is, the more intense the vibration of inner tubes are than that of outer tubes, and the more the vibration tends towards noncoaxial. (c) 2010 American Institute of Physics. [doi:10.1063/1.3480987]