Carbon nanotube (CNT) based continuous fiber, a CNT assembly that could potentially retain the superb properties of individual CNTs on a macroscopic scale, belongs to a fascinating new class of electronic materials with potential applications in electronics, sensing, and conducting wires. Here, the fabrication of CNT fiber based stretchable conductors by a simple prestraining-then-buckling approach is reported. To enhance the interfacial bonding between the fibers and the poly(dimethylsiloxane) (PDMS) substrate and thus facilitate the buckling formation, CNT fibers are first coated with a thin layer of liquid PDMS before being transferred to the prestrained substrate. The CNT fibers are deformed into massive buckles, resulting from the compressive force generated upon releasing the fiber/substrate assembly from prestrain. This buckling shape is quite different from the sinusoidal shape observed previously in otherwise analogous systems. Similar experiments performed on carbon fiber/PDMS composite film, on the other hand, result in extensive fiber fracture due to the higher fiber flexural modulus. Furthermore, the CNT fiber/PDMS composite film shows very little variation in resistance (approximate to 1%) under multiple stretching-and-releasing cycles up to a prestrain level of 40%, indicating the outstanding stability and repeatability in performance as stretchable conductors.