A drug delivery device is formed from an elastic sleeve deployed around a core, with first and second edge portions inwardly inverted. When a fluid is introduced between the core and the sleeve, the sleeve inflates to form a reservoir with a pressure of the fluid pressing the inwardly-inverted extremities portions against the core. The device is preferably anchored by providing a stem of conformable material which is depressed by pressure applied by adjacent edges of a layer of tissue to achieve tissue-wedged anchoring of the device.
