This paper presents a theoretical investigation of the axisymmetric free vibrations of an isotropic thin oblate spheroid shell. The analysis depends on the Rayliegh – Ritz's method. The non – shallow shell theory is used for the analysis. The analysis based on considering the oblate spheroid as a continuous system constructed from two spherical shell elements matched at the continuous boundaries.
Throughout the results, it is shown that when the eccentricity reaches zero, an exact thin sphere solution is emerged and when the eccentricity equals one an exact thin circular plate solution is emerged. Therefore, the eccentricity of an oblate shell at medium value lies between these two values.
It was found that the Rayleigh – Ritz's method is suitable for all eccentricities, while the literature showed that the Rayleigh's method is suitable for eccentricities less than 0.6.