A non-penetrating roof structure or system and method comprising a roof deck, a plurality of retainers connected to the roof deck between the margins thereof, and a cover membrane extending over the roof deck and the retainers. The cover membrane is generally flexible. A kit for connecting the cover member to the roof deck comprising the battans and retainers is also provided. The cover membrane is affixed to the deck at the margins and connected to the roof deck between the margins by the retainers. The cover member is imperforate over the retainers and the deck.