Choose a nice dress made of synthetic fabric that is less likely to wrinkle, like a cotton, polyester, tencel and spandex blend.
Reduce friction and wrinkles by wrapping your dress in gift wrap tissue or a plastic dry cleaning bag before packing it in your backpack.
Roll the dress before loading it into your backpack to reduce creases.
Bundle-wrap the dress with your other clothes to reduce both wrinkles and creases. Wrap each clothing item separately around a soft core object. Begin with items that do not wrinkle easily, and finish with larger items like your nice dress. Secure the bundle in your backpack.
Pack the dress in the bottom of the pack, or in an external zippered pouch, when traveling. Shake the dress out when you arrive at your destination.