Method of loading a dunnage conversion machine and sheet stock material useful therein

A supply of stock material for a dunnage conversion machine includes two plies of sheet stock material wound into a roll or fan-folded into a stack. Each ply has disposed on a corresponding leading or trailing end thereof an adhesive layer and a removable release liner covering the adhesive layer. When applied to a leading end of the supply, the adhesive layer is applied to opposing, outwardly-facing surfaces of the respective plies. When a supply of stock material is almost spent, the operator removes the release liners from both plies to expose respective adhesive layers, and then interposes the leading end of a new supply between the plies of the trailing end of the almost-spent supply and presses the layers together to attach the plies of the new supply to respective plies of the almost-spent supply, for conversion into dunnage.