Abstract: Searches for the lepton flavour violating decay tau(-) -> mu(-)mu(+)mu(-) and the lepton flavour and baryon number violating decays tau(-) -> (p) over bar mu(+)mu(-) and tau(-) -> p mu(-)mu(-) have been carried out using proton-proton collision data, corresponding to an integrated luminosity of 1.0 fb(-1), taken by the LHCb experiment at root s = 7 TeV. No evidence has been found for any signal, and limits have been set at 90% confidence level on the branching fractions: B(tau(-) -> mu(-)mu(+)mu(-) < 8.0 x 10(-8), B(tau(-) -> <(p)over bar>mu(+)mu(-)) < 3.3 x 10(-7) and B(tau(-) -> p mu(-)mu(-)) < 4.4 x 10(-7). The results for the tau(-) -> (p) over bar mu(+)mu(-) and tau(-) -> p mu(-)mu(-) decay modes represent the first direct experimental limits on these channels.