Abstract: A search for the rare decays B-s(0) -> pi(+) pi-mu(+) mu-and B-0 -> pi(+) pi-mu(+) mu-is performed in a data set corresponding to an integrated luminosity of 3.0 fb(-1) collected by the LHCb detector in proton-proton collisions at centre-of-mass energies of 7 and 8 TeV. Decay candidates with pion pairs that have invariant mass in the range 0.5-1.3GeV/c(2) and with muon pairs that do not originate from a resonance are considered. The first observation of the decay B-s(0) -> pi(+) pi-mu(+) mu- and the first evidence of the decay B-0 -> pi(+) pi-mu(+) mu-are obtained and the branching fractions, restricted to the dipion-mass range considered, are measured to be B(B-s(0) -> pi(+) pi-mu(+) mu(-)) =(8.6 +/- 1.5(stat) +/- 0.7(syst) +/- 0.7 (norm)) x 10(-8) and B(B-0 -> pi(+) pi-mu(+) mu(-)) =(2.11 +/- 0.51(stat) +/- 0.15(syst) +/- 0.16(norm)) x10(-8), where the third uncertainty is due to the branching fraction of the decay B-0. -> J/Psi(mu(+) mu(-)) K*(892)(0)(-> K+ pi(-)), used as a normalisation.