System for covering flat surfaces that is installed on support structures formed by support poles (2) maintained in position by a network of tie-rods (3), both the support poles and the tie-rods being fixed on the surface by means of suitable pins. Said system comprises a plurality of pairs of elongated support elements (6,6') having a lower portion positioned on such poles (2) and being joined together in raised position in proximity to their upper end, to form a plurality of pairs of slopes on which protection nets or protection sheets (7) are positioned, which in open position cover the area below the support structure and which in closed position are compact and amassed between adjacent poles (2) of the same row; the movement from the open position to the closed one and vice versa being obtained through the sliding of the sheet along the support elements by means of movement means.