A model is proposed to describe the evolution of the amorphization process driven by mechanical grinding. This model considers the interface controlled growth of the disordered regions at the boundaries between the crystallites (unlike the classical nucleation and growth theory, the growing particles are thus concave which affects the kinetic equation). The validity of this model has been tested for the amorphization process of mechanically alloyed Fe-Nb-B system at different frequencies. Predictions of the model are in agreement with the experimental results and values of the linear growth rate and the thickness of the starting disordered layer are obtained.