The cactus group is the fundamental group of the real locus of the Deligne-Mumford moduli space of stable rational curves. This group appears naturally as an analog of braid group in coboundary monoidal categories; the main example of this is the category of crystals where the cactus group acts on tensor product of crystals by crystal commutors. We define an action of the cactus group on the set of Bethe vectors of the Gaudin magnet chain (for Lie algebra sl_2) and prove that this action is isomorphic to the action of cactus group on the tensor product of sl_2-crystals. We also relate this to the Berenstein-Kirillov group of piecewise linear transformations of the Gelfand-Tsetlin polytope. Some conjectures generalizing our construction will be discussed.