Device for laying a flexible material in the form of a web, such as a strip of film, of felt, of nonwoven or of fleece, along a re-entrant or interior profiled corner formed by abutting surface strips (4, 4') of two surfaces (5, 5') that are substantially mutually perpendicular, the laying being effected by said device being moved along a direction parallel to the direction of extension of the profiled corner, said device comprising, at least, a means for supporting and progressively unwinding a roll or reel of the flexible material in the form of a web, a means for frontally guiding and applying the web of material into the edge of the corner, and at least one means for returning the progressing web of material between the roll or the reel and the guiding and application means, these means (6, 7, 8) being mounted together on a frame that forms the common supporting structure of the device and is provided with at least one handling member, such as a handle and/or a shaft, for example, said device also comprising a pressing means with a main body that is configured and arranged so as to carry out, during the movement in the course of a laying operation, a surface application of each of the two longitudinal flanks (12, 12') of the web of material, said flanks being situated on either side of the fold (2"), respectively against one of the abutting surface strips (4, 4') of the two surfaces (5 and 5'), which are situated on either side of the edge, specifically by way of sliding linear pressure, said pressing means being mounted elastically on the supporting structure and being offset with respect to the frontal guiding and application means, in the opposite direction to that of the movement during a laying operation, the device being characterized in that the guiding and application means is configured to form a longitudinal fold (2") in the progressing web of material before it is applied into the edge. said device comprising, at least, a means for supporting and progressively unwinding a roll or reel of the flexible material in the form of a web, a means for frontally guiding and applying the web of material into the edge of the corner, and at least one means for returning the progressing web of material between the roll or the reel and the guiding and application means, these means (6, 7, 8) being mounted together on a frame that forms the common supporting structure of the device and is provided with at least one handling member, such as a handle and/or a shaft, for example, said device also comprising a pressing means with a main body that is configured and arranged so as to carry out, during the movement in the course of a laying operation, a surface application of each of the two longitudinal flanks (12, 12') of the web of material, said flanks being situated on either side of the fold (2"), respectively against one of the abutting surface strips (4, 4') of the two surfaces (5 and 5'), which are situated on either side of the edge, specifically by way of sliding linear pressure, said pressing means being mounted elastically on the supporting structure and being offset with respect to the frontal guiding and application means, in the opposite direction to that of the movement during a laying operation, the device being characterized in that the guiding and application means is configured to form a longitudinal fold (2") in the progressing web of material before it is applied into the edge.