Determining the Elastic Properties of SWNTs has been one of the most hotly disputed areas of nanotube study in recent years. On the whole, SWNTs have are stiffer than steel and are resistant to damage from physical forces. Pressing on the tip of the nanotube will cause it to bend without damage to the tip or the whole CNT. When the force is removed, the tip of the nanotube will recover to its original state.  Quantizing these effects, however, is rather difficult and an exact numerical value cannot be agreed upon.
The Young's modulus (elastic modulus) of SWNTs lies close to 1 TPa. The maximum tensile strength is close to 30 GPa.
Reference: M.-F. Yu et al., Phys. Rev. Lett. 84, 5552 (2000).
The results of various studies over the years has shown a large variation in the value reported. In 1996, researchers at NEC in Princeton and the University of Illinois measured the average modulus to be 1.8 TPa.  This was measured by first allowing a tube to stand freely and then taking a microscopic image of its tip. The modulus is calculated from the amount of blur seen in the photograph at different temperatures. In 1997, G. Gao, T. Cagin, and W. Goddard III  presented a talk at the Fifth Foresight Conference on Molecular Nanotechnology where they reported three variations on the Young's Modulus to five decimal places that were dependent on the chiral vector. They concluded that a (10,10) armchair tube had a modulus of 640.30 GPa, a (17,0) zigzag tube had a modulus of 648.43 GPa, and a (12,6) tube had a value of 673.94 GPa. These values were calculated from the second derivatives of potential. Using these two different methods, a discrepency arises.
Further studies were conducted. In 1998, Treacy et al.  reported an elastic modulus of 1.25 TPa using the same basic method as done two years earlier. This compared well with the modulus of MWNTs (1.28 TPa), found by Wong et al. in 1997. Using an AFM, they pushed the unanchored end of a freestanding nanotube out of its equilibrium position and recorded the force that the nanotube exerted back onto the tip.  In 1999, E. Hernández and Angel Rubio showed using tight-binding calculations, the Young's Modulus was dependent on the size and chirality of the SWNT, ranging from 1.22 TPa for the (10, 0) and (6, 6) tubes to 1.26 TPa for the large (20,0) SWNT. However, using first principal calculations, they calculated a value of 1.09 TPa for a generic tube. 
The previous evidence would lead us to assume that the diameter and shape of the nanotube was the determining factor for it's elastic modulus. However, when working with different MWNTs, Forró et al. noted that their modulus measurements of MWNTs in 1999 (using AFM) did not strongly depend on the diameter, as had been recently suggested. Instead, they argued that the modulus of MWNTs correlates to the amount of disorder in the nanotube walls. However, their evidence showed that the value for SWNTs does in fact depend on diameter; an individual tube had a modulus of about 1 TPa while bundles (or ropes) of 15 to 20 nm in diameter had a modulus of about 100 GPa.
It has been suggested that the controversy into the value of the modulus is due to the author's
interpretation of the thickness of the walls of the nanotube. If the tube is considered to be a solid
cylinder, then it would have a lower Young's modulus. If the tube is considered to be hollow, the
modulus is gets higher, and the thinner we treat the walls of the nanotube, the higher the modulus
will become.