In this paper, a method is proposed to find the optimal transverse shear function (OTSF) in a specific plate theory. Starting from the polynomial unified framework (PUF) of the transverse shear function, genetic algorithm (GA) has been used to find the best independent parameters in PUF, to obtain the OTSF. Taking the bending of functionally graded rectangular plates as an example, the errors of OTSF and other transverse shear functions are compared. The results show that the error of OTSF is the smallest. The accuracy of plate theory can be controlled by changing the independent parameters in PUF. Therefore, this method is expected to reduce the increasing number of transverse shear functions in new literature. In addition, by studying the results of two plate theories (the difference is whether thickness stretching is considered), it can be concluded that the accuracy of plate theories can be significantly improved by considering the effect of thickness stretching.