The process of spinning and machining for heavy plates has the problems of a large amount of machining, large springback, and easy cracking. Aiming to address these issues, we proposed a deep drawing forming method for a plate with differential thickness to manufacture an integral ellipsoid component with a thin zone in the middle and a thick zone in the periphery. The plate with a differential thickness was initially produced through machining, followed by the execution of deep drawing deformation. During the deformation process of plates with differential thickness, the thin zone is prone to rupture defects. Therefore, a hydroforming method utilizing an elastic auxiliary plate was adopted to solve this problem. Through mechanical analysis and deep drawing experiments, the influences of hydraulic pressure and elastic auxiliary plate on the distributions of thickness and strain were studied, and the influence of friction on hydroforming was analyzed. The results indicate that increasing the hydraulic pressure and setting elastic auxiliary plates can increase the interfacial friction, reduce the thickness thinning rate, and improve the thickness distribution and deformation uniformity within the thin zone. When the hydraulic pressure is 5.2 MPa and the thickness of the elastic plate is 5 mm, the maximum thickness thinning rate of the ellipsoid shell is 8.8%, which is 34% lower than that of the ellipsoid shell obtained via conventional deep drawing.