Carbon nanotubes (CNTs) are ideal structures for use as reinforcement fibres in composite materials, due to their extraordinary mechanical properties, in particular high Young's modulus ( E similar to 1 TPa). Usually the high value of E is taken as granted for all types of carbon CNTs. Here we demonstrate that multi-walled carbon nanotubes ( MWCNTs) produced by catalytic chemical vapour deposition (CCVD) have low moduli ( E < 100 GPa) independently of their growth conditions. We attribute this to the presence of structural defects. Additional high-temperature annealing failed to improve the mechanical properties. This study urges a better control of the growth process in order to obtain high strength CCVD grown MWCNTs suitable for reinforcement in large-scale industrial applications.