Abstract: The integral equations of rotating disc with variable thickness are derived bymeans of the ring fundamental solution of elacticity. Then the integral equations are solved by spline function method. Also, this method is applied to the rotating variable-thickness disc with circular hole. Its computing program is so simple as to work on the IBM-PC computer. Due to the spline interpolation, very high accuracy of the numerical solution can be achieved even if few elements are chosen, The numerical results obtained by this method is almost completely consistent with the exact solution. Obviously, this method overcomes the shortcomings of the finite element method or finte difference method in need of solving huge systems of algebraical equations.