A search for the Standard Model Higgs boson produced in association with a vector boson with the decay $H\rightarrow \tau\tau$ is presented. The data correspond to 20.3 fb$^{-1}$ of integrated luminosity from proton-proton collisions at $\sqrt{s} = 8$ TeV recorded by the ATLAS experiment at the LHC during 2012. The data agree with the background expectation, and 95% confidence-level upper limits are placed on the cross section of this process. The observed (expected) limit, expressed in terms of the signal strength $\mu = \sigma/\sigma_{\mathrm{SM}}$ for $m_\mathrm{H} = 125 GeV$, is $\mu <$ 5.6 (3.7). The measured value of the signal strength is $\mu = 2.3\pm1.6$.