[en] Self-consistent models are constructed for prolate elliptical galaxies. Using only two integrals of motion, the energy E and the angular momentum about the axis of symmetry (L/sub z/), analytical solutions are derived. In projection they resemble the spindle-shaped galaxies NGC 3115 and 7332. The flattening of these systems arises from a suppression of the angular momentum about the long axis. The models have a logarithmic singularity in the central surface brightness and exhibit a strong peak in the central velocity dispersion, thus providing another example of the effect of anisotropic velocity dispersion on the observed properties of the central regions of galaxies