To verify the existing theory, non-propagating crack(NPC) does not exist in Ti which fulfills the good conditions for being of NPC, NPC detection in Ti was tried out. Also, the conception of fatigue limit in Ti and a main cause for NPC being were inquired. NPC was detected in both sharp notch root ( $ ho$=0.02mm) and micro pit (diameter = 0.25mm) which held fast to the end under stressing of fatigue limit. Therefore, the existing theory was identified as mistake. But, NPC can not be detected in smooth specimen. This fact would be due to the presumption that NPC is very small or crack does not initiate in smooth specimen. Anyway, the fatigue limit of Ti does not correspond to critical stress of crack initiation but correspond to critical stress of NPC growth. Measurement on the COD of NPC in Ti showed that the crack tip was closed even under the peak stress level at fatigue limit. But, after stress relieving annealing crack tip was opened. Consequently, compressive residual stress which is induced around the crack tip is considered to be the factor causing the NPC being.