Recent work has shown evidence of cyclical phase transformations taking place during mechanical alloying. Cyclical phase transformations resemble dynamic equilibrium in the sense that both equilibrium and non-equilibrium phases are simultaneously present during milling, but phase fractions vary during cyclical transformations. A brief thermodynamic and kinetic account is first discussed to establish the criteria for cyclical transformations. A two-dimensional molecular dynamic work is then presented to demonstrate cyclical phase transitions between an equilibrium and a non-equilibrium phase during mechanical alloying. A model binary crystal made of 57 Lennard-Jones atoms is studied to illustrate cyclical transitions between an equilibrium rhombus and a non-equilibrium square phase.