Little information currently exists on designing highly efficient ball mills for producing mechanically alloyed material. This work is an attempt at understanding the mechanisms of alloying in order to design better equipments. The problem of efficiency of mechanical alloying is investigated numerically by simulating the dynamics of a shaker ball mill. The model consists of two major parts: shaker ball mill dynamics simulation and the grinding model. The dynamics simulation is used to find out how the number of collisions, the total kinetic energy, and the rate of energy dissipation in the system depend on both the frequency and amplitude of vibrations and on the number of balls. The model of an ideal gas is used to validate the dynamics model. Two models are developed to simulate the distribution of radii of particles during the grinding process: a statistical model and a deterministic one, representing an average-case behavior of the statistical model. Both models compare favorably against each other as well as against experimental results.