We study the classical electronic motion of the hydrogen atom near a plane metal surface, using the Hamiltonian with exact form of the atom - surface potential. The case is considered. The phase space of the system is separated into the regions of vibrational and rotational motion. Although the system is nonintegrable, for large values of nucleus - surface distance ( at E = -1 au) the motion is close to regular in the whole of phase space. However, at smaller distances chaotic trajectories appear. Instability of some trajectories at smaller distances is such that the electron can be captured onto the surface.