A stabilization seal is used with existing cannulas for forming a gas-tight seal with tissue in a body wall The stabilization seal includes a cylindrical inflatable elongate tube having a graduated wall-thickness that is thicker in a central region and thinner in a distal-end region. The tube includes a sealing cuff, having an inflation port, for sealing around a cannula. Application of inflation pressure greatly expands the distal-end region while the central region expands slightly. Another embodiment of a stabilization seal includes an inflatable thread that is used with a cannula having a helical channel on its outer surface. An inflatable tube is wound into the channel. A distal end of the tube includes a gas-tight seal and a proximal end of the tube includes an inflation port In the uninflated condition the nested tube is flush with the channel. Inflating the tube enlarges the cannula assembly.