The development of high damping materials is important in the modern world, in order to suppress noises and to avoid vibrations in automobiles etc. In such development researchers are paying keen attention to the use of the relaxation type internal friction peak in martensite, because the peak is stable at constant temperature. Such a relaxation type peak was first found in Ti-Nibased alloys in 1960's, and was interpreted in various ways in the past, such as dislocation relaxation, dislocation-point defect relaxation or hydrogen relaxation, etc. Recently we proved by critical experiments in Ti 50 Ni 50-x Cu x alloys that both twin boundaries and hydrogen are indispensable for the appearance of the relaxation peak. In order to check the generality of the result, other shape memory alloys such as Ti-Ni-Fe, Ti-Ni-Pd, Ti-Pd, Mn-Cu, Au-Cd, Cu-Al-Ni etc. were investigated from this viewpoint by using DMA. As a result, the relaxation peak was observed in most of the alloys, except for Cu-Al-Ni alloy. By assessing the previous mechanisms proposed, we will discuss the possible mechanism for the relaxation peak in martensite. Based on these investigations, a guideline for obtaining high damping materials is also suggested.