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Some shirts are designed to be tucked, some to be untucked. How to tell the difference easily?: Dress Smarter: When to Tuck Your Shirt.
IMPORTANT INFORMATION
Remember the wrists rule: if a shirt is longer than your wrists and reaches down to your palm, then it must be tucked. If it reaches only down to your wrists, then it must be untucked (or else it will come off all the time). Some shirts now have a medium cut. Just don't buy them, they look wrong if untucked and if you tuck them they'll keep coming out all the time. Half tucks (tucking only the right or left part ) are only ok if you really want to look like a drunk man going straight for prison.
Unless you have a prominent belly, you should buy your shirts with a slim fit, making sure they more or less stick to your torso and are not baggy. Baggy shirts can never look elegant or cool, they simply look messy and they simply can stay tucked even if you try.
Another tip: if a shirt is curving lower down at the back than at the front, then it is meant to be used untucked. Shirts for tucking have a straight cut at the bottom, they are the same length in front or at the back.