A tubular structure having variable support includes a tubular member and a structural support member with a flexible tubular member over the structural support member, such that the flexible tubular member can engage and disengage or squeeze and release the structural support member. The structural support member can be a tubular mesh, stent, framework, skeleton, braid or other flexible framework. A fluid passage can be used to inflate and deflate the flexible tubular member. Methods of assembly and methods of use are also described.
