Abstract. In this paper, the R-function theory(RFT) is applied to solve the free vibration of slip clamped trapezoidal shallow spherical shell on Winkler foundation. Firstly the fundamental solution of the biharmonic operator, the boundary equation and the R-function are used to construct the quasi-Green's function. Then the model governing differential equation of the problem is reduced to the Fredholm integral equation of the second kind by Green's formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation by the R-function. A numerical example shows that this method is an effective numerical method.

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