The Shakedown analysis area of a functionally graded (FG) Bree plate subjected to coupled constant mechanical loading and cyclically varying temperature is analyzed and optimized by using the genetic algorithm (GA) method. The shakedown theorem could take into account the material hardening. The variations of the material properties in the thickness of FG Bree plate are characterized by exponential distributions. In order to obtain the best mechanical properties in the FG plate, the distribution of the reinforcement particles volume fraction is optimized through GA method. A numerical example is presented, which demonstrates the validity of the developed method in shakedown analysis of FG Bree plate.