The reconstrainment band includes a hollow generally tubular shaped bandhaving proximal and distal ends andhaving an exterior surface for engaging a stent and an interior surface forengaging a delivery tube. The exterior surface has atleast one fin projecting therefrom along the longitudinal axis of the band.The fin has at least one obtusely shaped surface relativeto the longitudinal axis and facing one of the ends. The reconstrainment bandis included in a delivery device for intraluminallypositioning and deploying a radially distensible stent. Reconstrainment of apartially deployed stent is provided by the deliveryde-vice.