A supply of inflatable pouches includes an inflatable web having two sheets sealed to define a series of inflatable in chambers having a closed distal end and an open proximal end providing an inflation port for each of the chambers. The chambers are arrayed in a transversely. The inflatable web includes a longitudinal fold defining two juxtaposed inflatable panels. A series of transverse seals bond the panels together to form a connected series of inflatable pouches between pairs of the transverse seals. The inflatable web includes a series of slits, each slit extending transversely in the two juxtaposed inflatable panels from the longitudinal fold for at least one inch. Each slit of the series is between adjacent inflatable pouches.