A material behaves elastically when it returns to its original size after being stretched.
String elasticity is a property that seems to be widely misunderstood. There is a belief that new steel strings permanently elongate before they settle down and can be relied upon to tune to a stable pitch. It is even commonly recommended that this supposed stretching-in can, and should be accelerated, by grabbing the string somewhere around its middle and forcibly yanking it away from the guitar. This is an unnecessarily violent thing to do and can damage both the string and the guitar. It may result in a permanent kink in the string by flexing it beyond its elastic limit. Once this happens, the strings harmonic purity is compromised, even though the kink may seem to disappear when the string is tuned to pitch. Pulling on the strings can cause the ball ends to bite hard into the bridge plate, accelerating wear in this area. Any tuning instability for a new string is not due to permanent elongation, but to settling and slippage at the bridge and tuners. Careful and correct installation of new strings will minimise and even eliminate this movement. [emphasis added]