The boson peak in metallic glasses is modeled in terms of local structural shear rearrangements. Using Eshelbys solution of the corresponding elasticity theory problem (J. D. Eshelby, Proc. Roy. Soc. A241, 376 (1957)), one can calculate the saddle po
int energy of such a structural rearrangement. The neighbourhood of the saddle point gives rise to soft resonant vibrational modes. One can calculate their density, their kinetic energy, their fourth order potential term and their coupling to longitudinal and transverse sound waves.
