Shallow buoyant, surface plumes in coastal waters sometimes develop by nearly radial spreading from a continuous source, such as at a river mouth. Such plumes often display a ring structure where buoyant water is concentrated between fronts at both the leading and trailing edges of the expanding ring. These rings often occur in multiple, concentric forms. A model of the radial, time dependent spreading of a shallow buoyant layer over a motionless, deep ambient layer is developed. It includes fronts as discontinuities and treats the remainder of the plume flow as inviscid, gravitational spreading controlled by nonlinear, internal waves. Calculations by the method of characteristics are presented that show the evolution of a clear ring structure. The combination of rapid spreading in the radial geometry together with reflection of internal waves off the frontal boundary at the plume leading edge is shown to be necessary for ring formation. A mechanism is suggested for the formation of multiple rings through the shear flow instability inherent in radial spreading.