A press device, e.g., a shoe press device, for treating a sheet of material, e.g., paper or cardboard, in an elongated press gap elongated in a travel direction of the sheet of material. The press device may include a flexible roll jacket that runs around a stationary carrier, an opposing face that forms the elongated press gap with the flexible roll jacket, and at least one of a hydrodynamically and hydrostatically lubricated support element supported on the carrier. The support element may include a compression face adapted to a shape of the opposing face and at least one cloth belt guided through the elongated press gap. The support element may further include an entry face for the flexible roll jacket and for the cloth belt and positioned before the compression face in the travel direction of the sheet of material. A lubricant aspiration device is located before the support element in the travel direction, and is spaced from the roll jacket during normal operation.