Use of a superconducting traveling wave accelerating (STWA) structure with small phase advance per cell for future high energy linear colliders may provide an accelerating gradient 1.2-1.4 times larger [1] than a standing wave structure. However, the STWA structure requires a feedback waveguide [1]. Recent tests of a 1.3 GHz model of a single-cell cavity with waveguide feedback demonstrated an accelerating gradient comparable to the gradient in a single-cell ILC-type cavity from the same manufacturer [2]. This opened the way for traveling wave cavity technology. A 3-cell traveling wave cavity was developed [3,4] and is being manufactured at AES, Inc [5].The tuner requirements for the traveling wave cavity are considered in this paper. The results of detailed studies of the mechanical and tuning properties of the superconducting resonator with a 3-cell traveling wave accelerating structure are also presented. The tuner design presented here was developed based on the results of these studies. A tuner test stand was developed and measured at room and liquid nitrogen temperatures under a 300 kg load to prove the tuner design feasibility. Test data are presented and discussed.