Several members of the public have posted photos to the MacRumors site that appear to show the problem. A reporter for the Geek.com news site also reported his phone had warped.
Other mobiles have bent in the past.
It is not yet clear if the iPhones 6’s aluminum shells make them particularly vulnerable.
Even so, the claims have been reported across tech blogs as well as mainstream media including the Independent, the Washington Post, India Today and the Sydney Morning Herald.
Twitter users have also posted thousands of comments about the claims, using the hashtag Bentgate.
Apple is marketing both the iPhone 6 and the larger iPhone 6 Plus as the thinnest smartphones it has released – with both models less than 0.3in (0.76cm) thick.
Some iPhone owners have posted comments to the company’s own website about the earlier models becoming misshapen, and the Cult of Mac site notes that owners of Samsung, Blackberry and other handsets have also reported instances of bent devices.
However, it is unusual for the issue to be given so much attention so soon after a launch – the new iPhones went on sale only on September 19.
Insurer Square Trade had declared the new iPhones “more durable” than their predecessors after carrying out tests, but did not carry out “bendability” checks.
YouTube show Unbox Therapy’s own stress test – which involved an unusual amount of pressure being applied – suggested that the iPhone 6 Plus was easier to bend than the plastic-coated Samsung Galaxy Note 3.
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