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In this paper, we investigate $\tau^- \to e^-(\mu^-) K\bar{K}(K\bar{K}=K^+K^-,K^0\bar{K}^0)$ decays in the framework of the RPV SUSY model. We discussthe tree level contribution of the sparticles $\tilde{\nu}$ and $\tilde{u}$ tothese decay branching ratios. In the two channels, the $\tilde{\nu}$-mediatedchannel is more sensitive to the parameter product$|\lambda^{'*}_{i22}\lambda_{i31(2)}|$ than the $\tilde{u}$-mediated channel to$|\lambda^{'*}_{1(2)j2}\lambda'_{3j2}|$. And the parameter product$|\lambda^{'*}_{i22}\lambda_{i31(2)}|$ is severely constrained to the order of${\cal O}(10^{-5})$ by the experiment data with $m_{\tilde{\nu}}=100 GeV$,which is one order of magnitude more stringent than before. In the calculationof hadronic matrix elements, the resonant effects are large than those ofnon-resonant terms. Especially, the resonant contribution of scalar meson$f_{(980)}$ plays a dominate role in $\tilde{\nu}$-mediated channel.

RPV SUSY effects in $\tau^- \to e^-(\mu^-) K\bar{K}$ Decays