Abstract: With the deepening application of digital technology on architectural design, many buildings using techniques of classical and free curved surfaces appear at home and abroad.As an important classical surface, the ellipsoidal surface can be used more widely than the spherical surface.However, the practical engineering employs more spherical surfaces in the geometric modeling.Discussions about how to mesh the ellipsoidal surface elegantly are rarely seen in domestic literatures, for geometric calculation and analysis of ellipsoidal surfaces are relatively complicated.Besides, it is difficult to solve the differential equation of inclined path of the ellipsoidal surface.This paper adopts the viewpoint of the intrinsic geometry to establish and solve three different differential equations of inclined path of the ellipsoidal surface.Then the analytical solution, the series solution and the numerical solution are obtained.The conformal correspond of the rotational ellipsoid and the plane is discussed and the equidistant-surface equations are presented.Using the method of NURBS and the Rhinoceros-Platform, the process is presented in three-dimensional view through specific examples.