  Supersymmetric Twin Higgs models allow for reducing the fine-tuning with
respect to Minimal Supersymmetric Standard Model by protecting the mass of the
Higgs boson by additional, accidental global symmetry. This class of models
introduce numerous new states, some of which might be candidates for dark
matter. Since those reside in twin sector, they are not charged under Standard
Model gauge group. We proposed twin stau as a candidate for dark matter. Even
though twin stau is charged under twin electromagnetism, since supersymmetric
partners obtain large masses from supersymmetry breaking they can easily escape
bounds for self-interacting dark matter. The mass of twin stau which reproduces
correct relic abundance is usually between 300 and 500 GeV. This scenario can
be probed by future direct detection experiments such as Lux-Zepelin.
