Structures with planar geometries and analyzing their vibration behavior have attracted special and deep consideration these days. In this research for investigating the orthotropic plates' vibration behavior, finite difference method with error orders of and are implemented. At first, the classical and analytical solutions are surveyed and then relevant equations, needed for numerical analysis, are extracted for those mentioned error orders. Finally the obtained natural frequencies for both modes are compared non-dimensionally. Also simulation with ANSYS software is performed for validation of the results and confirmation of the proposed method's accuracy.