Based on the stress distribution formulae of a semi-infinite plane under a single concentrated force，the in-plane stress distribution formulae of a thin disk under a self-balanced in-plane concentrated force system is obtained by using the principle of superposition of external loads. The stress distribution of the thin disk under the self-balanced in-plane distributed force system is further obtained by the integral calculation. Taking the product of the Chebyshev polynomial and the boundary functions as the admissible functions，the eigenvalue equations of transverse free vibration and buckling of a thin disk under arbitrary in-plane static loads are derived by means of the Ritz method. The eigenvalue equations are numerically solved to obtain the natural frequencies and buckling loads. The fast convergence and the high accuracy of the method are verified by comparison with the results the product of pow er series and Fourier series as admissible functions and finite element method.