Greene Hall was completed in 1966 as a co-ed “pod-style” 37,329-square-foot, three-story dormitory. It was named in honor of Lake Greene, a long-time physical plant director. In 2023, the hall was added to the National Register of Historic Places. In 2024, SAU received 1.454 million in grants from the Arkansas Natural and Cultural Resources Council (ANCRC) for restorations, which began in the summer of 2025. Amenities for the hall include a computer lab, vending, a laundry room, luxury vinyl floors throughout, Wi-Fi, a common area, and AC. The hall offers traditional-style community bathrooms on each floor. Greene Hall has the Living Learning Communities of Living Greene, which focuses on recycling and living a clean, eco-friendly lifestyle, and First Year Experience. The hall houses several Mulerider athletic teams, including Baseball and Men’s Track and Cross-Country.