South Street Park Amphitheatre

Yes, Sheffield has an open-air amphitheatre. It is easily accessible from the rear entrance of Sheffield Train Station or by crossing over the Supertram bridge at Park Square roundabout. 

Under the shadow of Park Hill, it boasts one of the very best views of the city centre, and has been used for performances, screenings and installations - but mainly is used by folks hanging out on nice, sunny days.