Elbow Bursitis, also known as Olecranon Bursitis, is a swelling of a fluid-filled sac in the back of your elbow. This sac is called the "olecranon bursa." You have similar sacs near other large joints throughout your body. They act as cushions between your bones and your soft tissues. Normally they have a small amount of fluid inside them. But sometimes they can swell. That is called "bursitis."