Collisional ionization between two Rydberg atoms in relative motion is examined. A classical trajectory Monte Carlo method is used to determine the cross sections associated with the Penning ionization. The dependence of the ionization cross section on the magnitude and the direction of orbital angular momentum of the electrons and the direction of the Laplace-Runge-Lenz vector of the electrons is studied. For a given magnitude of angular momentum, the calculations indicate a difference in the ionization cross section of a factor ∼ 2.5 between the orientation with the highest and the lowest ionization cross section. The case of exchange ionization is examined and its dependence on the magnitude of angular momentum is studied.