Aims. Inelastic processes in low-energy Si + H and Si + + H − collisions are treated for the states from the ground state up to the ionic state, in order to provide rate coefficients needed for non-LTE modeling of Si in cool stellar atmospheres. Methods. Electronic molecular structure is determined using a recently proposed model approach based on an asymptotic method in combination with available ab initio potentials. Nonadiabatic nuclear dynamics are treated by means of a combination of multichannel formulas and the branching-probability-current method, based on the Landau-Zener model for nonadiabatic transition probabilities. Results. Cross sections and rate coefficients for inelastic processes in Si + H and Si + + H − collisions for all transitions between 26 low-lying states plus the ionic state are calculated. It is shown that the highest rate coefficient values correspond to the excitation, deexcitation, ion-pair formation, and mutual neutralization processes involving the Si(3p4p 3 D), Si(3p3d 3 F), Si(3p4p 1 D), Si(3p3d 3 P), Si(3p4p 1 S), and the ionic Si + + H − states. These processes are likely to be important in non-LTE modeling.