A computing method is proposed to solve the two-dimensional Helmholtz operator, and the method is used to solve the vibration problem of thin plates on Pasternak foundation with complex boundary shape conditions. By using the shape function obtained by R-function, the Bessel function, the basic solution and boundary conditions of the two-dimensional Helmholtz operator, a quasi-Green function satisfying the homogeneous boundary conditions is constructed. The integral kernels are obtained by using the properties of Bessel function, and then the two-dimensional Helmholtz operator is transformed into integral equation by Green's formula. The appropriate boundary equation is selected by using R-function theory to eliminate the singularity, in which Bessel function is transformed into corresponding numerical expression. The method is applied to analyze the free vibration problem of thin plates on Pasternak foundation. The numerical examples show that the method is an effective numerical method.