The effect of a surface on electronic fluctuations in anisotropic metals is studied theoretically. The Coulomb interacton of the electron-hole excitations is taken into account self-consistently. A system consisting of the Boltzmann equation for electronic fluctuations and the Maxwell equations for the interaction field is solved with appropriate boundary conditions. The cross section of inelastic light scattering is calculated. The scattered light observed out of the metal is a result of the collective electron interaction with radiation inside the metal. The scatteirng cross section consists of the bulk contribution of electron-hole pairs and plasmons, which differs from the scattering by an infinite metal only in the effect of the penetration of radiation in the skin layer. The surface contribution to the cross section is attributed to the electromagnetic excitations of the nonradiative into-vacuum surface plasmons (the sharp peak) and the radiative surface plasmons (the continuum with a peak).