Motivated by the variety of rings around planets in our solar system, and arguably in other planetary systems
as well, we will analytically treat the venerable problem of investigating the potential of a massive annular distribution. In
a first approximation, we can consider the mass distribution as homogenous. Actually, a more realistic model should take
into account the non-isotropy of density.In this work, we establish an analytical elliptic form of the potential generated by
an anisotropic matter distribution. The study of the dynamical behavior is performed within the Hamiltonian formulation,
which allows us to derive some orbits of the test particle.