Inelastic processes in low-energy Be+H and Be^+^+H^-^ collisions are treated for the states from the ground state up to the ionic state, with the aim to provide rate coefficients needed for non-LTE modeling of beryllium spectra in cool stellar atmospheres. The electronic molecular structure is determined by using a recently proposed model quantum approach that is based on an asymptotic method. Nonadiabatic nuclear dynamics is treated by means of multichannel formulas, based on the Landau-Zener model for nonadiabatic transition probabilities.