Abstarct: The application of bending plates is widely used in civil, aerospace and mechanical engineering. Finite element analysis of the bending plane has many complexities. A large number of solutions have been presented baxsed on solving the problems arising in the analysis of bending plates, and many efforts have been made in order to expand its application. In this regard, researchers have used various methods for the static analysis of bending plates. The use of solutions that establish the condition of compatibility between adjacent components and the condition of establishing the displacement function in the governing differential equation in order to achieve greater convergence and accuracy of answers while performing fewer calculations has always been the focus of researchers. The loading of structures is dynamic in many cases. By analyzing the free vibration the dynamic characteristics of the plate can be determined and for this reason, it is very important. In order to prevent the phenomenon of resonance which has irreparable damage to the structures it is necessary to determine the natural frequencies of the plane. In the present study, finite element relationships for two bending elements baxsed on the Trefftz function and Reisner-Mindlin theory have been utilized and the free vibration of the bending plane is evaluated by establishing the mass matrix for them. In order to obtain the mass matrix in the second element, a separate function has been used. In this regard, by solving numerous numerical tests, the natural frequencies of the plate with different schematics and boundary conditions for thin and thick plates have been obtained, and the answers of other researchers' methods are used for comparison. The results of this analysis include the following: In a square plate whose four sides are on a simple support, in a 16 × 16 fine grid with an increase in the ratio of the length to the thickness of the plate up to 106, the frequency responses for these two elements are not diverged and shear locking problem in it. have not occurred, as a result, these two elements have performed well in the range of bending thin plates. Also, in a square plate with a 4x4 coarse grid, whose four sides are on a simple support, there was no disturbance in the frequency response due to the change of the grid shape. In the other case, the free vibration of the square plate is analyzed by placing one of its sides on the supporting support and keeping the other sides free, for the cases where the corner angle of the plate is 90, 60, and 30 degrees. Also, in this research, it will be shown that the frequency responses for these two elements in the rectangular plane will have a faster convergence speed than the other elements as the grid becomes smaller. The sides parallel to the x-axis of this free plane and the other sides are on the simple support.