Aiming at the problem of the axially- compressed buckling of the small- scale carbon nanotubes in multi-physical fields,a mechanical model for the coupled fields is proposed based on the nonlocal elasticity theory.First,a buckling governing equation of the multi- walled carbon nanotubes subjected to thermo- electro- mechanical loadings is obtained based on the nonlocal elasticity theory and by using the elastic shell model,which considers the van der Waals forces between adjacent nanotubes and the effects of the surrounding elastic medium.Then,the analytical solution to the axially critical buckling load of double- walled carbon nanotubes is derived.Finally,the small- scale effects on the axially critical buckling load are discussed by means of numerical analysis.It is found that,with a large coefficient of the small- scale effects,the critical buckling load based on the nonlocal elasticity theory is markedly different from that based on the classical elasticity theory,which indicates that the classical elasticity theory is no longer applicable in a small- scale range.