A machine for inflating and sealing an inflatable structure having a longitudinal edge generally comprises a drive, an inflation nozzle, a sealing device, and a sheet engagement device. The machine may define an engaging assembly and an opposing assembly. The drive may be rotationally coupled to the sheet engagement device such that when the drive rotates, the engagement device also rotates. The sheet engagement device may comprise one or more engagement rollers which may have a plurality of teeth thereon. A first plurality of rollers and a second plurality of rollers comprising the engagement rollers may intermesh between a drive roller and a backing roller on the longitudinal edge of the inflatable structure. Thereby, the sheets of the inflatable structure may be engaged together and the length of the longitudinal edge may contract to facilitate inflation. The resulting inflated inflatable structure may comprise an embossed longitudinal edge.