The organisation said the cases add weight to long-held allegations that the US has held detainees in secret in its war on terrorism.
“We fear that what we have heard from these two men is just one small part of the much broader picture of US secret detentions around the world,” said Sharon Critoph, an Amnesty researcher.
“Not only do such conditions encourage torture and ill-treatment, but to be ‘disappeared’ from the face of the earth without knowing why or for how long is a crime under international law and is an experience no-one should have to go through.”
The two Yemeni men, interviewed by Amnesty International, are currently in jail in their own country.
They reported being held in solitary confinement by the US for over a year and a half, and during this time they rarely saw daylight, were mostly shackled and in handcuffs, and were not given a chance to communicate with lawyers or their families.
They said they had no idea which country they were in.
The organisation spoke to the two friends, Salah Nasser Salim Ali and Muhammad Faraj Ahmed Bashmilah, in June.
They had been living in Indonesia when they were separately detained in 2003: one in Jordan and the other in Indonesia.
Saleh reported being flown to Jordan where both were tortured, then flown to unknown jails where they were held in solitary confinement without charge.
Neither men knew the other had also been detained.
They both said they were held in an underground facility several hours from Jordan for six to eight months, before being taken to another place, around three hours away by plane.
They said their first jail was underground and surrounded by high walls, and the second was a modern prison run by US officials, which also appeared to be underground.
“These men were stripped of their dignity, at times beaten, spat on, deprived of sleep and threatened with sexual abuse and electric shocks,” said Amnesty USA’s executive director William F Schulz in a statement.
“Their testimony will hopefully shed light on US detention centres just as sinister, yet less well-known, than Guantanamo.”
The White House has in the past denied allegations it has secret detention facilities, saying terrorism suspects are only held at Guantanamo Bay in Cuba, and in Iraq and Afghanistan.