AbstractHighly flattened objects may appear in early stages as well as in late stages of stellar evolution. The calulation of their axisymmetric gravitational potential in spherical coordinates requires a lot of computer time. In this paper we compare iterative solutions of the Poisson differential equation with direct evaluations of the Poisson integral with respect to accuracy and time consumption. further, we derived a fast direct method which is superior in computer time to the discussed methods whereas its accuracy remains nearly unchanged.