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The exclusive weak decay of $\Lambda_b \to \Lambda \gamma$ and $\Lambda_b \to\Lambda l^{+} l^{-}$ are investigated in the Applequist-Cheng-Dobrescu model,which is an extension of the standard model in presence of universal extradimensions. Employing the transition form factors obtained in the light-conesum rues, we analyze how the invariant mass distribution, forward-backwardasymmetry and polarization asymmetry of $\Lambda$ baryon of these decay modescan be used to constrain the only one additional free parameter with respect tothe standard model, namely, the radius $R$ of the extra dimension. Our resultsindicate that the Kaluza-Klein modes can lead to approximately 25% suppressionof the branching ratio of $\Lambda_b \to \Lambda \gamma$, however, theircontributions can bring about 10% enhancement to the decay rate of $\Lambda_b\to \Lambda l^{+} l^{-}$. It is shown that the zero-position offorward-backward asymmetry of $\Lambda_b \to \Lambda \mu^{+} \mu^{-}$ issensitive to the compactification parameter $R$ in this scenario, while themeasurement of polarizations of $\Lambda$ baryon in the $\Lambda_b$ decays isnot suitable to provide some valuable information for the universal extradimension model.

Rare decays of $\Lambda_b \to \Lambda \gamma$ and $\Lambda_b \to \Lambda l^{+} l^{-}$ in universal extra dimension model