A search for the lepton-flavour violating decays B s 0 e± and B0 e± is performed based on a sample of proton-proton collision data corresponding to an integrated luminosity of 3 fb1, collected with the LHCb experiment at centre-of-mass energies of 7 and 8 TeV. The observed yields are consistent with the background-only hypothesis. Upper limits on the branching fraction of the B s 0 e± decays are evaluated both in the hypotheses of an amplitude completely dominated by the heavy eigenstate and by the light eigenstate. The results are @@B(B0se±)<6.3(5.4)×109@@B(Bs0e±)<6.3(5.4)×109 \frac{@}{@}\mathrm{\mathcal{B}}\left({B}_s^0\to {e}^{\pm }{\mu}^{\mp}\right)<6.3(5.4)\times 1{0}^{-9} and @@B(B0se±)<7.2(6.0)×109@@B(Bs0e±)<7.2(6.0)×109 \frac{@}{@}\mathrm{\mathcal{B}}\left({B}_s^0\to {e}^{\pm }{\mu}^{\mp}\right)<7.2(6.0)\times 1{0}^{-9} at 95% (90%) confidence level, respectively. The upper limit on the branching fraction of the B0 e± decay is also evaluated, obtaining @@B(B0e±)<1.3(1.0)×109@@B(B0e±)<1.3(1.0)×109 \frac{@}{@}\mathrm{\mathcal{B}}\left({B}^0\to {e}^{\pm }{\mu}^{\mp}\right)<1.3(1.0)\times 1{0}^{-9} at 95% (90%) confidence level. These are the strongest limits on these decays to date. Open image in new window