Aleve is a brand of naproxen, a nonsteroidal anti-inflammatory drug (NSAID) used to relieve pain, inflammation, and stiffness caused by conditions such as arthritis, tendinitis, bursitis, menstrual cramps, and gout. It is available in both over-the-counter and prescription forms. ALEVE is the brand name for naproxen sodium, which is a salt form of naproxen. It is one of the most commonly used NSAIDs and is available in many countries around the world.