What causes pain in butt that radiates down both legs?

A pinched nerve: The most common reason for back pain that shoots down the leg is a pinched nerve which may be due to: 1. A herniated disc 2. Spinal stenosis 3. A slipped vertebra (spondylolisthesis) 4. Other reasons (tumor, infection, etc.) seek medical attention if there is progressive worsening of pain, numbness, weakness, tingling, or bowel/bladder issues.

Several things : Including a disc herniation. There are other possibilities. Peripheral vascular disease & spinal stenosis both can cause pain into a leg mimicking sciatic pain as can other issues like hip & knee arthritis. Other causes of nerve compression in the spine due to a tumor, infection or fracture can cause this pain. Pyriformis syndrome can also cause radiating leg pain as can sacroiliac joint issues.