The surface magnetization of metals associated with electrons whose orbits are tangential to the metal boundary is investigated, taking into account anisotropy in the energy spectrum of conduction electrons. It is shown that the angular dependence of magnetization has peculiarities determined by the curvature of the Fermi surface at the reference points. Explicit expressions have been obtained for the surface magnetic susceptibility of electrons in bismuth, and appropriate numerical estimates of its value have been made. ©1997 American Institute of Physics.