Summary: This paper deals with the Stokes flow of the arbitrary oblate axisymmetrical body by means of constant density and quadratic distribution function approximation for the method of continuous distribution of singularities. The Sampson spherical infinite series are chosen as fundamental singularities. The convergence, accuracy and range of application of both two approximations are examined by the unbounded Stokes flow past the oblate spheroid. It is demonstrated that the drag factor and pressure distribution both conform with the exact solution very well. Besides, the properties, accuracy and the range of application are getting better with the improving of the approximation of the distribution function. As an example of the arbitrary oblate axisymmetrical bodies, the Stokes flow of the oblate Cassini oval are calculated by these two methods and the results are convergent and consistent. Finally, with the quadratic distribution approximation the red blood cell, which has physiologic meaning, is considered and for the first time the corresponding drag factor and pressure distribution on the surface of the cell are obtained.