Wide range of planar structures in new technologies has attracted special consideration. In this research vibration behavior of plates with non-linear edges is investigated by means of finite difference (FD) method. For this issue, classical and analytical solutions for plates with linear edges were analyzed and mutual equations, needed for numerical calculation were extracted. By expanding the current equations to the non-linear edged plates (e.g. elliptical plates), natural frequencies of this special structure were analyzed numerically and computer simulation with ANSYS software. According to the un-existence of classical or analytical solution for this special configuration, closeness of numerical analysis and computer simulation confirms the accuracy of selected method in this study.