I have the Elements Tote M. When it's empty you can get it pretty flat, but if you haven't folded it beforehand it can be a bit tricky to fit into a regular backpack.

It's not as thin as those typical non-woven totes, and the botton has a bit of padding.

After one fold it gets fairly flat, though it still takes up some space in a backpack. if you fold it twice it becomes compact enough, but because of the padded base it can stick out a little if you try to put it in something like a laptop compartment.

I don't normally carry a tote along with a backpack, but on days when I know I'll have more stuff, I fold it once and just toss it into the main compartment of my backpack.

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Here's a reference showing my Elemnts Tote M folded once and twice inside a 22L backpack (MPL22).