The apparent witness, 69, who has been named only as Jill, made the confession in an interview which has been posted online by a UFO researcher.
Claiming she was aged around 10 at the time, she said she and a friend handled the material, that could not be cut or burnt and recovered its shape if crumpled up for a number of days.
The video was posted on YouTube by UFO researcher Mary Joyce, who runs a website called Sky Ships over Cashiers.
Roswell has been at the heart of the UFO scene since in July 1947 the military sensationally announced in a press release it had found the remains of a crashed flying saucer in the desert nearby.
But the following day it retracted the statement, saying it was in fact a damaged US Air Force air balloon.
Witnesses later came forward to say there had been alien bodies within the "crashed craft", which along with the wreckage were then taken to the mysterious top-secret Area 51 military base in Nevada.
In the new interview Jill says she saw the material in 1957.
Her father was a pilot with the US Air Force at the time based at Wright-Patterson Air Force base.
To read more and view the video, click here