The kink signature of charged tracks is predicted in some SUSY models, and it is very characteristic signal at collider experiments. We study the kink signature at LHC using two models, SUSY models with a gravitino LSP and a stau NLSP, and R-parity violating SUSY models with a stau (N)LSP. We find that a large number of kink events can be discovered in a wide range of the SUSY parameters, when the decay length is O(10-10^5)mm. Model discrimination by identifying the daughter particles of the kink tracks is also discussed.Comment: 19 pages, 4 figures; Version published in JHEP; abstract refined, reference added and several minor corrections in tex
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