A cord retainer (10, 100, 140, 160) for retaining cords such as electrical power leads (32) and pneumatic hoses in an elevated position above the ground or floor. The cord retainer (10, 100, 140, 160) has a flexible web (14, 146, 168) with holes (30, 148) dimensioned to receive a cord (32) and substantially retained it against longitudinal movement with respect to the web (14, 146, 168) to the extent that the cord (32) is substantially prevented from sliding longitudinally in the hole (30, 148) under the force of its own weight or during normal installation of the cord (32), in two spaced apart cord retainers (10, 100, 140, 160). A series of frames 170, 180 and 190 are also provided for attaching the cord retainer (10, 100, 140, 160) structures on building and construction sites.