An elastic double-shell model based on continuum mechanics is presented to study the dynamic torsional buckling of an embedded double-walled carbon nanotube (EDWCNT). Based on the model, a condition is derived to predict the buckling load of the EDWCNT. It is shown that the buckling load of the EDWCNT for dynamic torsional buckling is no less than that for the static torsional buckling. Further, the effect of the van der Waals forces is discussed when an inner nanotube is inserted into an embedded outer one. In particular, the paper shows that, in the absence of the initial van der Waals forces, the buckling load of an EDWCNT is always in-between that of an isolated inner tube and of an embedded outer nanotube, which is different from the result obtained by neglecting the difference of radii. This indicates that disregarding the difference of the radii of the double-walled nanotubes can not properly describe the effect of the van der Waals forces between interlayer spacing.