Classical approach is a popular method that is used in analysis of structures including bending plates, but these plates can have highly irregular geometry and contains holes or subjected to loading irregularity, the analysis is further complicated and the classical approaches are not valid. Thus, the Finite Element Method is used to control the accuracy and it is needed for more difficult problems. In the present study Fourier series theory as classical approach and finite element method of analysis were discussed and the numerical examples of a simply supported and fixed supported square steel plate are used to compare them. The results obtained with general public software LISA that uses FEM was plotted according to the elements types, both quadrangular and triangular elements. Their convergence was verified with the values obtained from classical approach to valid the results of FEM from LISA. The results shown the conformity with existing theories that the more discretization the more the reality is approached, the convergence error of 5% was taken as the maximum error for elements types and meshes to be used for highly sophisticated plate systems. The ratios of element size to the size of the whole square plate to be used for general cases of square plate dimensions were established.