An apparatus and method for percutaneous placement of access tubes, such as feeding and drainage tubes, vascular catheters, and the like, comprises an elastic access tube in an internal stylet. The stylet is received within a central lumen of the access tube and is used to axially elongate the tube, resulting in a reduced diameter. In a first embodiment, the diameter of the access tube is reduced sufficiently so that it can be placed through a relatively narrow penetration and so that it will radially expand by an amount sufficient to cause a tight anchor and seal against the penetration when the stylet is removed. In a second embodiment, the stylet has a sharpened distal tip which extends beyond the distal end of the access tube when in its axially extended configuration. The sharpened tip allows self-introduction of the assembly of access tube and stylet. In a third embodiment, a distal portion of the access tube is covered with a lubricous sheath. The lubricous sheath facilitates use of the assembly in combination with a dilation member which is radially expanded when the assembly of access tube and stylet is introduced therethrough.