A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes.Taking the geometric nonlinearity of structure deformation,the effects of van der Waals forces as well as the non-coaxial curvature of each nested tube into account,the nonlinear parametric vibration governing equations are derived.Numerical results indicate that the double-walled nanotube(DWNT) can be considered as a single column when the van der Waals forces are suffciently strong.The stiffness of medium could substantially reduce the area of the nonlinear dynamic instability region,in particular,the geometric nonlinearity can be out of account when the stiffness is large enough.The area of the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes. A multiple-elastic beam model based on Euler-Bernoulli-beam theory is presented to investigate the nonlinear dynamic instability of double-walled nanotubes. Making of geometric nonlinearity of structure deformation, the effects of van der Waals forces as well as the non-coaxial curvature of each nested tube into account, the nonlinear parametric vibrational governing equations are derived. Numerical result indicates that the double-walled nanotube (DWNT) can be considered as a single column when the van der Waals forces are suffciently strong. the stiffness of medium could substantially reduce the area of ​​the nonlinear dynamic instability region, in particular, the geometric nonlinearity can be out of account when the stiffness is large enough. the area of ​​the principal nonlinear instability region and its shifting distance aroused by the nonlinearity both decrease with the increment of the aspect ratio of the nanotubes