A sleeved composite pipe or piling structure formed of an elongated polyethylene pipe or tube of high-density polyethylene (HDPE) or another polyethylene material installed over a substantially rigid and incompressible hollow metal pipe or solid wood core having an outer diameter that is the same or slightly larger than a normal inside diameter of the polyethylene pipe or tube when measured in a relaxed state at ambient temperature. The polyethylene pipe or tube is, for example, a HDPE 3408 material formed of virgin PE 3408 resin as specified in ASTM D3350 with UV protection, and the pipe is produced to ASTM A-3408. The metal pipe core can be ferrous or nonferrous pipe.