  The exclusive rare radiative $B$-decays are studied in the framework of the
relativistic quark model based on the quasipotential approach in quantum field
theory. The large recoil momentum of the final vector meson allows for the
expansion of the decay form factor in inverse powers of the b-quark mass. This
considerably simplifies the analysis of these decays. The $1/m_b$ expansion is
carried out up to the second order. The form factor of \btok decay is found to
be $F_1^{B\to K^* \gamma}(0)=0.32\pm 0.03 $ and it leads to $BR(B\to K^*\gamma
)= (4.5\pm 1.5) \times 10^{-5}$, which is in agreement with the recent CLEO
data. The form factors of the decays \btorho, \bstophi and \bstok are also
considered. The relation between rare radiative and semileptonic $B$-decays
into light vector meson is discussed.
