A delivery system includes an inflatable delivery balloon formed with a plurality of constraining elements which create constrained regions in a body portion of the balloon, interposed between unconstrained regions. The constrained regions create recesses for receiving a medical device or part of a medical device. The constraining elements are preferably formed by woven or braided material, advantageously embedded within the wall of the inflatable balloon. The constraining elements provide a structure that will not flatten upon inflation of the balloon and also a structure which can readily be folded or wrapped for endoluminal delivery purposes, and which retains flexibility of the delivery device.