The Snoek relaxation, a specific point-defect induced anelastic relaxation phenomenon, is characteristic of an internal friction peak in bcc metals with interstitial solutes. Such internal friction mechanism has not been applied in the development of high damping alloy while grain boundary and twin boundary featured anelastic relaxations are applied in some high damping alloys. In this paper, the fundamental principles and experimental results concerning the Snoek relaxation are reviewed, and the feasibility to apply the Snoek relaxation mechanism into high damping alloys is discussed. Due to the peak-shape behavior in the Snoek relaxation type damping, composition design of a high damping alloys should takes temperature position, broadness and also peak height into account. Ti-Nb-O and Ti-V-Cr-O alloys are designed and fabricated by CCLM casting in our laboratory. It is conformed that the damping behaviors of the alloys are of Snoek relaxation type showing obvious frequency and temperature dependence. While the broadened damping peak caused by the substitutional solutes is advantage to improve the temperature stability of damping capacity, a large concentration of interstitial solute and texture control are required to improve the reduced damping capacity.