Newly documented Ring Moat Dome Structures (RMDSs), low mounds typically several hundred meters across with a median height of ~3.5 m and surrounded by moats, occur in the lunar maria. They appear to have formed synchronously with the surrounding mare basalt deposits. It has been hypothesized that they formed on the surfaces of lava flows by the extrusion of magmatic foams generated in the flow interiors as the last stage of the eruption and flow emplacement process. We develop a theoretical model for the emplacement and cooling of mare basalts in which the molten cores of cooling flows are inflated during the late stages of eruptions by injection of additional hot lava containing dissolved volatiles. Crystallization of this lava causes second boiling (an increase in vapor pressure to the point of supersaturation due to crystallization of the melt), generating copious quantities of vesicles (magmatic foam layers) at the top and bottom of the central core of the flow. Flow inflation of many meters is predicted to accompany the formation of the foam layers, flexing the cooled upper crustal layer, and forming fractures that permit extrusions of the magmatic foams onto the surface to form domes, with subsidence of the subjacent and surrounding surface forming the moats. By modeling the evolution of the internal flow structure we predict the properties of RMDSs and the conditions in which they are most likely to form. We outline several tests of this hypothesis.