  Electromagnetic waves, solving the full set of Maxwell equations in vacuum,
are numerically computed. These waves occupy a fixed bounded region of the
three dimensional space, topologically equivalent to a toroid. Thus, their
fluid dynamics analogs are vortex rings. An analysis of the shape of the
sections of the rings, depending on the angular speed of rotation and the major
diameter, is carried out. Successively, spherical electromagnetic vortex rings
of Hill's type are taken into consideration. For some interesting peculiar
configurations, explicit numerical solutions are exhibited.
