A substantially flat roof has elongated log-shaped members arranged horizontally in adjacent, side-by-side relation. Each log-shaped member has a contoured upper surface, and the contoured upper surfaces of adjacent members define a space between them that tapers from a maximum width at the highest elevation of the contoured surfaces to a minimum width where the contoured surfaces of adjacent log-shaped members are closest together. Elongated inserts are arranged between the contoured upper surfaces. Each insert has a wide portion that abuts an adjacent pair of the contoured upper surfaces at a relatively high elevation, and tapers to a narrow portion that abuts the contoured surfaces at a relatively low elevation substantially at the ends of the adjacent pair of log-shaped members. Rain falling on the roof drains by gravity from the contoured upper surfaces to the inserts and along the inserts towards their narrow portions and falls from the roof.