Sousse's main beach stretches for many kilometres to the north of the Medina. It was named after a local Muslim holy man and features some good sand. As it was mid winter when I was there, it wasn't being used as it was cold with a strong wind blowing off the sea but I expect it's heaving during the summer months.
The beach in Sousse starts just beyond the medina and stretches all the way north to Port el Kantaoui. It was March when we visited Sousse so the tourist season hadn't kicked off yet. I imagine it becomes much busier in the summer. Much of the beach is private, especially in the Zone Touristique which begins a couple of kilometres north of the medina.
North of the old city are the beaches, with sprawling resorts along them. I'm not a beach connsisseur, but from my travels I'd say they were average in quality, especially for the mediteranean sea. Though I stayed at one of the resort hotels when I was there, I'm pretty sure most of the beach is open to the public, so the chairs and the umbrellas already on the beach should be able to be used by anyone.
Be wary of men who try to sell you food on the beach, especially if you are in one of the resort hotels. They will indicate that it might be free of charge, giving you the food right away, and then charge $2 for some flat bread.
Sousse has really nice beaches, nice sea, really great place to relax, and the water is already warm early in the year!
Sousse is known by its nice beaches from El hana beah to chott meriem ...etc , places when you can enjoy the the blue sea and the wite sand :)