Localized spectral admittances of the large Martian volcanoes are modeled by assuming that surface and subsurface loads are elastically supported by the lithosphere. In order to model the case where the load density differs from that of the crust, a new method for calculating gravity anomalies and lithospheric deflections is developed. The modeled gravity anomalies depend upon the elastic thickness, crustal thickness, load density, and crustal density, and these parameters were exhaustively sampled in order to determine their effect on the misfit between the observed and modeled admittance function. We find that the densities of the Martian volcanoes are generally well constrained with values of 3200 ¿ 100 kg m-3, which is considerably greater than those reported previously. These higher densities are consistent with those of the Martian basaltic meteorites, which are believed to originate from the Tharsis and Elysium volcanic provinces. The crustal density is constrained only beneath the Elysium rise to be 3270 ¿ 150 kg m-3. If this value is representative of the northern lowlands, then Pratt compensation is likely responsible for the approximately 6-km elevation difference between the northern and southern hemispheres. The elastic thicknesses of the major Martian volcanoes (when subsurface loads are ignored) are found to be the following: Elysium rise (56 ¿ 20 km), Olympus Mons (93 ¿ 40 km), Alba Patera (66 ¿ 20 km), and Ascraeus Mons (105 ¿ 40 km). We have also investigated the effects of subsurface loads, allowing the bottom load to be located either in the crust as dense intrusive material or in the mantle as less dense material. We found that all volcanoes except Pavonis are better modeled with the presence of less dense material in the upper mantle, which is indicative of either a mantle plume or a depleted mantle composition. An active plume beneath the major volcanoes is consistent with recent analyses of cratering statistics on Olympus Mons and the Elysium rise, which indicate that some lava flows are as young as 10--30 Myr, as well as with the crystallization ages of the Shergottites, of which some are as young as 180 Myr.