Magmatic intrusions preferentially spread along interfaces marked by rigidity and density contrasts. Thus the contact between a lunar mare and its substratum provides a preferential location for subsequent magmatic intrusions. Shallow intrusions that bend the overlying layer develop characteristic shapes that depend on their radius and on the overlying layer flexural wavelength and hence on their emplacement depth. We characterize the topography of seven, previously identified, candidate intrusive domes located within different lunar maria, using data from the Lunar Orbiter Laser Altimeter. Their topographic profiles compare very well with theoretical shapes from a model of magma flow below an elastic layer, supporting their interpretation as intrusive features. This comparison allows us to constrain their intrusion depths and hence the minimum mare thickness at these sites. These new estimates are in the range 400-1900 m and are generally comparable to or thicker than previous estimates, when available. The largest thickness (⩾ 1700 m) is obtained next to the Hortensius and Kepler areas that are proposed to be the relicts of ancient volcanic shields.