The late stages of evolution of the primordial circumstellar disks surrounding young stars are poorly understood, yet vital to constraining theories of planet formation. We consider basic structural models for the disks around two similar to 10 Myr old members of the nearby RCrA association: RX J1842.9-3532 and RX J1852.3-3700. We present new arc second-resolution maps of their 230 GHz continuum emission from the Submillimeter Array and unresolved CO(3-2) spectra from the Atacama Submillimeter Telescope Experiment. By combining these data with broadband fluxes from the literature and infrared fluxes and spectra from the catalog of the Formation and Evolution of Planetary Systems Legacy program on the Spitzer Space Telescope, we assemble a multiwavelength data set probing the gas and dust disks. Using the Monte Carlo radiative transfer code RADMC to model simultaneously the spectral energy distribution and millimeter continuum visibilities, we derive basic dust disk properties and identify an inner cavity of radius 16 AU in the disk around RX J1852.3-3700. We also identify an optically thin 5 AU cavity in the disk around RX J1842.9-3532, with a small amount of optically thick material close to the star. The molecular line observations suggest an intermediate disk inclination in RX J1842.9-3532, consistent with the continuum emission. In combination with the dust models, the molecular data allow us to derive a lower CO content than expected, suggesting that the process of gas clearing is likely underway in both systems, perhaps simultaneously with planet formation.