Aiming at the problems of large deviation of plastic machining accuracy and different buckling instability loads of bionic egg-shaped shells under different flexible medium forming technologies, it is proposed to adopt unidirectional loading rubber bulging and granular medium bulging technologies of bionic egg-shaped shells. By comparing the plastic machining accuracy, geometric accuracy, and strength of bionic egg-shaped shells with different flexible mediums, the machining accuracy and overall quality of bionic egg-shaped shells can be improved. To explore the stress and strain conditions in different stages and regions of egg-shaped shell flexible medium forming technologies under the ideal condition of considering the thickness stress, the mechanical analysis of egg-shaped shell flexible medium forming technologies is carried out. The simulation analysis and experimental verification methods are used to analyze the forming process of egg-shaped shells with different flexible mediums and verify the accuracy of the numerical analysis model. Then, in order to master the influence of flexible medium forming technologies on the plastic deformation and quality of egg-shaped shells, the influence of different flexible medium forming technologies on the plastic machining accuracy, geometric accuracy, and strength of egg-shaped shells is researched. The study shows that the results of the numerical analysis of the egg-shaped shell flexible medium forming technology have an average error of no more than 11% with the test, and the numerical analysis model can be considered accurate. Moreover, the plastic machining accuracy of egg-shaped shell process parts and egg-shaped parts with granular medium is better than that of rubber medium. The maximum strain of the egg-shaped part is 4% higher than that of the rubber medium, and the maximum thinning rate is 13.9% smaller than that of the rubber medium. The geometric accuracy deviation of the egg-shaped part of the egg-shaped shell with the granular medium is 10% smaller than that of the rubber medium, and the process parts are also superior to the rubber medium. The buckling loads of the egg-shaped shell process parts with the granular medium are all higher than that of the rubber medium, and the buckling loads of the egg-shaped parts are slightly smaller than that of the rubber medium. However, taking into account the error of the egg-shaped shell flexible medium forming test, hydrostatic pressure test, and the overall buckling load distribution of the egg-shaped shell flexible medium forming process parts, it is considered that the overall strength of the egg-shaped shell with the granular medium is higher than that of the rubber medium.