An inflatable packer includes an elastomeric tubular body and an outer cover surrounding the body. An end member is also provided having a capped portion threadably engageable with an annular ring member, the ring member being secured to the end portion of the outer cover. A plurality of reinforcing elements are sandwiched between the cover and the body and have end portions terminating beneath the ring member. Finally, there is a mechanism for wedging the end portion of the reinforcing elements against the inner surface of the ring member in response to increased threaded engagement between the capped portion and the ring member to retain the elements in position beneath the ring member.