We have systematically analyzed the two-body weak radiative Lambda (b) -->
Lambda gamma decay of bottom baryon. The weak radiative decay proceeds thro
ugh W-exchange accompanied by a photon emission. Effective Lagrangian has b
een used for the W-exchange bremsstrahlung processes to estimate the long d
istance effect through pole. The short distance effect at the quark level (
b --> s gamma) is also estimated here. With these predictions we have final
ly obtained the branching ratio of Lambda (b) --> Lambda gamma as Br(Lambda
(b) --> Lambda gamma) = 2.3 x 10(-10) which is in close agreement with the
experimental results.