On google, I could find sentences like this:
His belly stretched the buttons on his shirt.
How do buttons get "stretched"? Buttons are normally not elastic. Could this be slang?
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As Maulik has rightly pointed out, the buttons are not stretched in terms of their dimensions: they do not assume oval shapes.
Taken at face value, the expression may seem illogical, but it has two great advantages: it is vivid and concise.
It makes us imagine the poor buttons feeling themselves stretched by the tension arising from the belly's outward push on the fabric of the shirt. On a lean man, the buttons would've found themselves hanging freely, but here, they have stretching forces applied to them from the left and from the right. Note the horisontal stretch creases appearing on the shirt in the photo provided by Maulik.
Sometimes stretch means to tighten.
We stretched the tent over the poles
We stretched a rope between two trees.
Stretch does not always mean to elongate in the process of tightening.
You might say the shirt was stretched around the buttons, but in this case we are emphasizing the stress on the buttons, in that the buttons are more likely to come off than the fabric is to tear, so the buttons are being stressed more although the shirt is more distorted by that stress.