A low profile secondary seal for sealing the space between the inner wall of a tank and a roof floating on a liquid product within the tank is of relatively simple, lightweight construction and of low profile so as to maximize the possible height of the floating roof within the tank. The seal includes a plurality of resilient support plates mounted in spaced-apart relation along the edge of the floating roof at first ends thereof and extending outwardly to opposite second ends thereof which are coupled to an elongated wiper assembly. The support plates are made of resilient material such as full hard stainless steel which maintains a desired shape in resilient fashion, so as to continuously resiliently bias the wiper assembly against the inner wall of the tank. The second ends of the support plates are pivotably coupled to the wiper assembly. Angled skid plates coupled to the wiper assembly engage the inner wall of the tank to facilitate movement of the wiper assembly thereover. A vapor barrier fabric, which has a first edge coupled to the rim of the floating roof and an opposite second edge coupled to the wiper assembly, is supported in a desired position by a plurality of fabric support straps disposed between the floating roof and the wiper assembly. The wiper assembly is durably constructed of low density polyethylene foam wrapped in PTFE Teflon fabric. The vapor barrier fabric is prepunched to facilitate bolting to the wiper assembly, and the location thereof on the outside of the seal facilitates inspection and replacement thereof, and shedding of rain water due to the angled orientation thereof.