A supply of inflatable pouches comprising: an inflatable web comprising two sheets having inner surfaces sealed to each other in a pattern defining a series of inflatable chambers , each chamber having a closed distal end and an open proximal end , the open proximal end providing an inflation port for each of the chambers , the chambers arrayed in a transverse orientation to a longitudinal dimension of the web ; a longitudinal fold in the web , which extends along the longitudinal dimension thereof such that the web is configured in the form of two juxtaposed inflatable panels joined together at the longitudinal fold ; and a series of transverse seals that bond the panels together to form a connected series of inflatable pouches between pairs of the transverse seals such that the connected series of inflatable pouches extends along the longitudinal dimension of the web , each inflatable pouch comprising one or more of the inflatable chambers ; characterized by a series of slits , each slit extending transversely in the two juxtaposed inflatable panels from the longitudinal fold for at least 2.54 centimeters, each slit being between adjacent inflatable pouches ; and a series of lines of weakness extending transversely across the web and between adjacent inflatable pouches ; wherein, as the inflatable pouches are inflated, the width of the inflatable pouches shortens as the inflation gas expands the chambers ; wherein the lines of weakness are situated in a region of the web that does not shrink; and wherein each slit of the series of slits corresponds with a respective line of weakness of the series of lines of weakness . an inflatable web comprising two sheets having inner surfaces sealed to each other in a pattern defining a series of inflatable chambers , each chamber having a closed distal end and an open proximal end , the open proximal end providing an inflation port for each of the chambers , the chambers arrayed in a transverse orientation to a longitudinal dimension of the web ; a longitudinal fold in the web , which extends along the longitudinal dimension thereof such that the web is configured in the form of two juxtaposed inflatable panels joined together at the longitudinal fold ; and a series of transverse seals that bond the panels together to form a connected series of inflatable pouches between pairs of the transverse seals such that the connected series of inflatable pouches extends along the longitudinal dimension of the web , each inflatable pouch comprising one or more of the inflatable chambers ; characterized by a series of slits , each slit extending transversely in the two juxtaposed inflatable panels from the longitudinal fold for at least 2.54 centimeters, each slit being between adjacent inflatable pouches ; and a series of lines of weakness extending transversely across the web and between adjacent inflatable pouches ; wherein, as the inflatable pouches are inflated, the width of the inflatable pouches shortens as the inflation gas expands the chambers ; wherein the lines of weakness are situated in a region of the web that does not shrink; and wherein each slit of the series of slits corresponds with a respective line of weakness of the series of lines of weakness . <EOS>