The polarization of the $Upsilon(1S)$, $Upsilon(2S)$ and $Upsilon(3S) $mesons, produced in $pp$ collisions at centre-of-mass energies $sqrt{s}$=7 and 8TeV, is measured using data samples collected by the LHCb experiment, corresponding to integrated luminosities of 1 and 2fb$^{-1}$, respectively. The measurements are performed in three polarization frames, using $Upsilontomu^+mu^-$ decays in the kinematic region of the transverse momentum $p_{T}(Upsilon)<30GeV/c$, and rapidity $2.2<y(Upsilon)<4.5$. No large polarization is observed.