A search for long-lived, massive particles decaying into dimuon pairs, in 32.9 fb-1 of data analyzed from the ATLAS detector is presented. Two signal models are considered: GGM SUSY, where the long lived particle mass is between 300-1000 GeV, and the dark photon model, where the ZD mass is between 20-60 GeV. An excess over the predicted background is observed in the GGM channel, however the angular/kinematic distributions of the excess vertices are consistent with a detec- tor/conditions related issue. A modified selection is used for the GGM channel which increases the signal sensitivity. 95% confidence level (CL) upper limits on the signal cross sections times branching fraction are set as a function of cτ for both benchmark models. The cτ limits for the GGM channel extend from 2.57-1050 cm, and the cτ limit for the ZD channel extends from 0.32-1572 cm. 95% CL upper limits on the ZD cross section are also set in the coupling-cτ plane, for a range of BF(H→ ZDZD).