Abstract: A practical method for analyzing stress singularity indexes was proposed for the problem of notch tips in bi-material functionally graded medium-thickness plates: the differential quadrature method (DQM). Firstly, according to the equilibrium equations in the cylindrical coordinate system and based on the series asymptotic expansion assumption about the displacement field at the tip of the notch, the eigenvalue problem of the ordinary differential equations (ODEs) with respect to the singularity exponent at the notch tip of functionally graded bi-material medium-thickness plates was derived, and the radial boundary condition of the notch was expressed as a combination of the singularity exponent and the characteristic angular function. Then, under the DQM theory, the eigenvalue problem of ODEs was transformed into a standard-type eigenvalue problem of generalized algebraic equations, and the stress singularity index at the notch tip under the corresponding boundary condition was calculated for only one time, and was verified to be valid by a numerical example. Finally, the stress singularity index of functionally graded and pure metal/pure ceramic hybrid plates was calculated with the DQM. The research indicates that, the mixing of pure ceramic plates and pure metal plates with functional gradient plates has different effects on the stress singularity index, respectively, with the change of the notch angle.