The dynamics of a mechanical subsystem interacting with an amorphous solid is studied. The Hamilton equations are transformed to a set of stochastic Langevin equations governing the random evolution of the coordinates of the subsystem particles. An explicit expression for the friction tenser is obtained which accounts both for the subsystem-solid interactions and for the thermal vibrations of the atoms of the amorphous solid. The possibility to calculate the diffusion coefficient of a Brownian particle in an amorphous solid is examined. Finally, a new approach for the description of the Brownian dynamics in liquids based on the results obtained for amorphous solids is proposed.