This paper applies the Adomian decomposition method (ADM) to the search for the approximate solutions to the problem of the nonlinear vibrations of multiwalled carbon nanotubes embedded in an elastic medium. A multiple-beam model is utilized in which the governing equations of each layer are coupled with those of its adjacent ones via the van der Waals inter layer forces. The amplitude–frequency curves for large-amplitude vibrations of single-walled, double-walled and triple-walled carbon nanotubes are obtained. The influence of changes in material constants of the surrounding elastic medium and the effect of changes in nanotube geometrical parameters on the vibration characteristics are studied by comparing the results with those from the open literature. This method needs less work in comparison with the traditional methods and decreases considerable volume of calculation, and it’s powerful mathematical tool for solving wide class of nonlinear differential equations. Special attention is given to prove the convergence of the method. Some examples are given to illustrate the determination approximate solutions of the proposed problem.