The edges of the film or films 8 and 9 acting as flexible covers are secured between, on the one hand, the walls of a seat 6 formed by a channel 4 and 5 formed in each of the two securing elements 2 and 3 and, on the other hand, an intermediate member 7, the whole assembly being clamped together by a sleeve 10 acting like a vice, which slides along the two securing elements 2 and 3 and which is positioned along these at regular intervals. The invention applies particularly to the covering of greenhouses, agricultural buildings and other spaces needing to be covered with a flexible material. <IMAGE>