Double wall carbon nanotubes (DWCNTs) have proven to have a very good structural stability when exposed to high static pressures. We report here on the study of DWCNTs after application of shock wave (dynamic) compression up to 36 GPa in a recovery assembly. TEM images of so-treated samples reveal a threshold between 19 and 26 GPa of shock wave compression above which significant structural damage is induced whereas only minor damage can be detected below. The threshold detected with TEM coincides well with the collapse pressure of DWCNTs previously reported [You et al., High Press. Res. 31, 186 (2011); Aguiar et al., Phys. Chem. C 115, 5378 (2011)]. Raman data demonstrate a gradual accumulation of structural defects via an increase in D-band to G-band intensity ratio (ID/IG-ratio) from ∼0.2 to ∼0.8 in going from the source CNT material to the nanotubes after compression to 36 GPa. Despite severe damage; the DWCNTs exposed to 36 GPa of shock wave compression survived which is evidenced by Raman spectra. The DWCNTs demonstrate a higher susceptibility to structural damage under dynamic than static pressure.