The Tyrrhena Patera highland volcano, Mars, is associated with a relatively well localized gravity anomaly and we have carried out a localized admittance analysis in the region to constrain the density of the volcanic load, the load thickness, and the elastic thickness at the time of load emplacement. The employed admittance model considers loading of an initially spherical surface, and surface as well as subsurface loading is taken into account. Our results indicate that the gravity and topography data available at Tyrrhena Patera is consistent with the absence of subsurface loading, but the presence of a small subsurface load cannot be ruled out. We obtain minimum load densities of 2960 kg m-3, minimum load thicknesses of 5 km, and minimum load volumes of 0.6 10^6 km3. Photogeological evidence suggests that pyroclastic deposits make up at most 30% of this volume, such that the bulk of Tyrrhena Patera is likely composed of competent basalt. Best fitting model parameters are a load density of 3343 kg m-33, a load thickness of 10.8 km, and a load volume of 1.7 10^6 km^3. These relatively large load densities indicate that lava compositions are comparable to those at other martian volcanoes, and densities are comparable to those of the martian meteorites. The elastic thickness in the region is constrained to be smaller than 27.5 km at the time of loading, indicating surface heat flows in excess of 24 mW m-2.