This paper provides an estimate of the thermal state of Martian lithosphere established since the formation of the shield volcanoes. Comparison of the spherical harmonic models of Martian topography derived using harmonics truncated at degrees 10, 11, 12, and 14 shows that the volcanoes have almost no contribution from harmonic coefficients of the topography less than degree 11. Therefore intermediate-scale surface topography and gravity anomalies of Mars, specified by harmonics of degree 11--50, are considered in this study. These harmonics are dominated by shield volcanoes, Alba Patera, and Isidis basin. The central part of Valles Marineris is also well defined by these harmonics. The strong correlation of the topography and gravity anomalies over these harmonics and the positive Bouguer anomalies of the volcanoes suggest significant excess masses beneath these surface features in addition to their topographic masses. This indicates that the Martian lithosphere has been strong enough to support both the topography and the internal excess masses. We determine the rigidity of the lithosphere beneath a given surface feature. The lithosphere is modeled by a thin elastic spherical shell that overlies an inviscid interior of higher density and is subjected to both surface and internal loads. The thickness of the shell and the magnitude of the internal load are calculated such that the deformed structure resulting from the flexure of the shell under both surface and internal loads gives rise to the observed topography and gravity anomaly. It is shown that the lithosphere beneath Elysium Mons, Alba Patera, and the central part of Valles Marineris can be modeled by elastic shells subjected to topographic loads alone, whereas the lithosphere beneath Olympus and Tharsis Montes cannot. Internal excess masses of at least 40%, and more likely 50%, of the topographic masses are required, and the lithosphere beneath must have an elastic core of ~100--80 km to support these volcanoes. The mean thermal gradient beneath this region of Tharsis is estimated to be ~7--10 K/km on the basis of the strength envelopes calculated using diabase rheology for the crust of 50 km thickness and olivine rheology for the underlying mantle. ¿ 2000 American Geophysical Union