A method for the construction of models of axisymmetric galaxies is presented. in this formulation we determine the distribution function corresponding to a given gravitational potential and the associated mass density distribution. Although the realization of the model is numerical, the underlying theory is analytic and exact. This method allows us to construct a wide range of models without having to use linear programming and a large amount of computer time. Here we present the results from the application of this method to the “perfect” oblate-spheroid mass model. A large class of valid self-consistent distribution functions which depend on three isolating integrals of the motion is found. the kinematics of many models are consistent with those observed for elliptical galaxies. in particular, models generated by this formulation are in agreement with the observed values of the ratio of the maximum projected rotational velocity to the velocity dispersion along the line of sight versus ellipticity.