It wrinkles. It's supposed to wrinkle. A linen suit or jacket without wrinkles is like a car without wheels: they just have to be there for it to work. And since we sit for long periods of time when we travel, our clothes tend to wrinkle even if they aren't supposed to.
So next time you want to travel wearing a suit or jacket, be like Cary Grant and try linen. That way when you arrive wrinkled, it looks natural. It looks right.
Of course your suit or jacket can't just be wrinkled, but it has to be wrinkled in the right areas: arms, back of the jacket (from sitting), at the back of the knees, etc. You want wrinkles, but you don't want to look like you just pulled the suit out of an overstuffed closet. The wrinkles must be specific.
I took a cue from Mr. Grant today and went all linen, since it was absurdly hot outside. I paired a jacket and trousers of slightly different colors as well as different types of linen to help contrast the look. Throw in a pink 1930s "Fruit of the Loom" tie, spectators and a Stetson and we've got a great summer kit.
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The jacket is made of smooth, finely woven linen while the trousers are a little more course and loosely woven. Both are lightweight and drape very well.
Give linen a try if you're travelling this summer.