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This work studies a possible approach to the prediction of lattice vibrations in crystals by means of multiple scattering theory. The method of choice for the description of the electronic structure is the technique of Korring-Kohn-Rostoker (KKR) in its expression as Green function method. To begin with, the work elaborates on numerical models of lattice vibrations and continues with the basic principles of linear response theory as well as the outline of the KKR. In the following sections, equations for the calculation of phonon spectra are worked out, based on these methods and using a spherical approximation of the ionic Coulomb potential. It is shown that this approximation - commonly used in multiple scattering theory - is not sufficient for a quantitative description of lattice vibrations. As opposed to this, a treatment of the full potential is necessary. The second part of this work deals with the KKR description of electron-phonon interactions in superconducting thin films and their influence on the critical temperature.