Today nanotubes are main parts of nano-machines who withstand against axial and vibrational loads. So, in this paper a mathematical model is presented to predict behavior of a spinning nanotube under axial load. For this purpose, classical thin shell theory and first order shear deformation shell theory are combined with nonlocal stress theory. The effect of rotation is considered by adding centrifugal and Coriolis forces in the formulations. Also, effect of axial compressive load is added in the formulation by considering buckling energy term. Equations are solved for both theories and numerical results are compared with the literature for validation. In the case of buckling of spinning nanotube there is not sufficient numerical results for comparison. So, Molecular dynamics (MD) simulation is done and its results in stationary and rotating conditions are compared with the mathematical model. These comparisons approved validity and accuracy of the mathematical models. Finally, effect of changing different parameters on the behavior of nanotube is investigated.