Abstract: A right-angle beam with fixed both ends is treated as an example to investigate the application of the mode synthesis method for calculation of higher-order natural frequencies. If the first 2 constrained mode shapes serve as the assumed mode shapes, some frequencies may miss and thus the second-order natural frequency cannot be calculated. If the assumed mode shapes include both the first 2 modal shapes and the first 2 constrained mode shapes, the first 3 natural frequencies can be calculated; and the assumed mode shapes include both the first 4 modal modes and the first 4 constrained mode shapes, the first 5 order natural frequencies can be calculated with the relative errors less than 5%.