Abstract We present a study of τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ , τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ , and τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ decays using a 666 fb − 1 data sample collected with the Belle detector at the KEKB asymmetric-energy e $^{+}$e − collider at and near a center-of-mass energy of 10.58 GeV. The branching fractions are measured to be: B ( τ − → π $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ )= (8 . 42 ± 0 . 00 +0 . 26 − 0 . $_{25}$) × 10 − $^{2}$, B ( τ − → K $^{−}$π $^{+}$π $^{−}$ν$_{τ}$ )= (3 . 30 ± 0 . 01 +0 . 16 − 0 . $_{17}$) × 10 − $^{3}$, B ( τ − → K $^{−}$K $^{+}$π $^{−}$ν$_{τ}$ )= (1 . 55 ± 0 . 01 +0 . 06 − 0 . $_{05}$) × 10 − $^{3}$, and B ( τ − → K $^{−}$K $^{+}$K $^{−}$ν$_{τ}$ )= (3 . 29 ± 0 . 17 +0 . 19 − 0 . $_{20}$) × 10 − $^{5}$, where the first uncertainty is statistical and the second is systematic. These branching fractions do not include contributions from modes in which a π $^{+}$π − pair originates from a K 0 S decay. We also present the unfolded invariant mass distributions for these decays. PACS numbers: 13.35.Dx, 12.15.Hh, 14.60.Fg 3 $^{30}$Novosibirsk State University, Novosibirsk $^{31}$Osaka City University, Osaka $^{32}$Panjab University, Chandigarh $^{33}$University of Science and Technology of China, Hefei $^{34}$Seoul National University, Seoul $^{35}$Shinshu University, Nagano $^{36}$Sungkyunkwan University, Suwon $^{37}$School of Physics, University of Sydney, NSW 2006 $^{38}$Tata Institute of Fundamental Research, Mumbai $^{40}$Toho University, Funabashi $^{39}$Excellence Cluster Universe, Technische Universit¨ at M¨ unchen, Garching $^{41}$Tohoku Gakuin University, Tagajo $^{42}$Department of Physics, University of Tokyo, Tokyo $^{43}$Tokyo Metropolitan University, Tokyo $^{44}$Tokyo University of Agriculture and Technology, Tokyo $^{45}$IPNAS, Virginia Polytechnic Institute and State University, Blacksburg, Virginia 24061 $^{46}$Yonsei University, Seoul