The buckling analysis of a simply supported single walled carbon nanotube embedded in an elastic medium with rotationally restrained boundary conditions is presented via nonlocal elasticity theory. A Fourier sine series incorporated with Stokes’ transformation is employed for the simulation of single walled carbon nanotube deflections. The Fourier coefficients for a embedded carbon nanotube having ends with rotational restraints are obtained by the substitution of deflection function and its derivatives into the governing differential equation. The explicit expressions are derived for the critical buckling loads by using nonlocal boundary conditions in terms of rotational restraint parameters. A detailed parametric investigation have been carried out to study the effects of the rotational spring parameters on the size-dependent stability characteristics of the carbon nanotube.