The reconstrainment band includes a hollow generally tubular shaped band having proximal and distal ends and having an exterior surface for engaging a stent and an interior surface for engaging a delivery tube. The exterior surface has at least one fin projecting therefrom along the longitudinal axis of the band. The fin has at least one obtusely shaped surface relative to the longitudinal axis and facing one of the ends. The reconstrainment band is included in a delivery device for intraluminally positioning and deploying a radially distensible stent. Reconstrainment of a partially deployed stent is provided by the delivery device.