  We study lepton flavour violating decays of neutralinos and sleptons within
the Minimal Supersymmetric Standard Model, assuming two and three generation
mixings in the slepton sector. We take into account the most recent bounds on
flavour violating rare lepton decays. Taking the SPS1a' scenario as an example,
we show that some of the lepton flavour violating branching ratios of
neutralinos and sleptons can be sizable (~ 5-10%). We study the impact of the
lepton flavour violating neutralino and slepton decays on the di-lepton mass
distributions measured at LHC. We find that they can result in novel and
characteristic edge structures in the distributions. In particular, double-edge
structures can appear in the e tau and mu tau mass spectra if ~tau_1 is the
lightest slepton. The appearance of these remarkable structures provides a
powerful test of supersymmetric lepton flavour violation at LHC.
