Al-Shehri, who was aboard American Airlines flight 11, the first jet to crash into the World Trade Centre in New York in 2001, is also seen on the tape.
IntelCenter, a US-based organisation that monitors radical websites, said it had a copy of the video which lasts 47 minutes.
The authenticity of the tape, which does not have moving images of bin Laden, could not be verified.
Praise
The video begins with a photograph of bin Laden in front of a brown backdrop.
In a voiceover, he is heard saying: "This talk of mine consists of some reflections on the will of a young man who personally penetrated the most extreme degrees of danger and is a rarity among men: one of the 19 champions, may Allah have mercy on them all."
Al-Shehri asserts in the tape that the US will suffer the same fate as the former Soviet Union and praises the losses the United States suffered in Somalia in the late 1990s.
"We shall come at you from your front and back, your right and left," he says.
"As for our own fortune, it is not in this world. And we are not competing with you for this world, because it does not equal in Allah's eyes the wing of a mosquito."
In an earlier tape released on Friday, bin Laden had mocked the US as "weak" and threatened to escalate the war in Iraq.
News of the latest video emerged before the US was to hold ceremonies to remember the dead from New York's Twin Towers, the US defence department headquarters in Washington and a hijacked jet that crashed into a field in Pennsylvania.