Carbon nanotubes (CNTs) are ideal structures for use as reinforcement fibres in composite materials, due to their extraordinary mechanical properties, in particular high Youngs modulus (E1 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.