The evolution and propagation of Gulf Stream warm core rings in a flat-bottom, β-plane ocean are studied using a three-dimensional primitive equation model. Rings are produced by a heat source that is turned on and off slowly in the upper 750 m of the water column. Besides an anticyclone in the upper ocean, a deep cyclone is generated below the surface eddy. In the first 30 days, the surface anticyclone moves slowly southwestward because of β dispersion and vorticity advection. In waters 4000 m deep, both the anticyclone and the cyclone intensify, and a barotropic vortex pair is formed. The vortex pair moves rapidly southeastward. Its propagation becomes steady and eastward after the cyclone sheds an eddy. The cyclone in the vortex pair moves away from the ring at the end of 6 months, and both vortices begin to propagate westward separately. Fluid to a depth of 3000 m, much deeper than that of forcing, is transported by the ring. The formation of a strong vortex pair is associated with the generation of relative vorticity in both vortices by unstable waves of the second azimuthal mode. In strong rings, the increase in vorticity could produce rapid propagation. Eastward propagation is a result of change in planetary vorticity and loss of relative vorticity during cyclone splitting. In waters shallower than 4000 m, the vortex pair is less stable and more vorticity is lost by cyclone splitting. There is still a rapid movement toward the south but the eastward propagation is weak. Rings in waters shallower than 4000 m are likely to remain on the continental slope off the U.S. East Coast and induce large amounts of momentum and mass transfer over the continental margin.