For the design problem of dynamic similitude models of an aero engine’s turbine discs, distorted scaling laws and structural size intervals of thin walled annular plates are established in the research. According to the governing equation, the geometrically complete scaling law of thin walled annular plates is firstly established. In order to determine accurate distorted scaling laws of thin walled annular plates, three significant principles are proposed and theoretically proved combining the governing equation and the sensitivity analysis. According to results of the sensitivity analysis, accurate distorted scaling laws of thin walled annular plates are obtained based on significant principles. In addition, structural size intervals of distorted scaling laws of thin walled annular plates are calculated by the numerical method. Finally, the previous six orders’ natural frequencies of thin walled annular plates are discussed as examples to verify the theory presented in this research, and distorted scaling laws of each order’s natural frequency are obtained and the corresponding structural size intervals are analyzed.