The conditions necessary for compressive and tensile failure of well bores drilled into crystalline rock can be adequately represented by simple elastic failure criteria, and analysis of well bore failure can provide constraints on the magnitudes of in situ stresses if the strength of the rock is known. When applied to several boreholes drilled into continental crust where there is relatively complete knowledge of stress magnitudes, these criteria enable us to predict the depth at which compressive failure of the well bores is observed. In oceanic crust, breakouts have been observed at depths below 700 m below sea floor in Deep Sea Drilling Project (DSDP) hole 504B, drilled into 5.9 Ma crust south of the Costa Rica Rift, and near the bottom of DSDP hole 395A, drilled into 7.3 Ma crust west of the Mid-Atlantic Ridge. In both cases the azimuth of maximum horizontal compressive stress is roughly perpendicular to the ridge axis. As the unconfined compressive strengths of basalt samples from DSDP hole 504B are generally above 200 MPa (Bauer and Handin, 1985), the existence of breakouts in DSDP holes 395A and 504B requires a highly compressional stress state, where Shmin≂Sv and SHmax≥100 MPa at about 500 m subbasement. These results are consistent with the state of stress inferred from compressional (strike-slip and reverse faulting) earthquake focal mechanisms in young oceanic crust. As ridge push forces are relatively small in young oceanic crust, we concur with previous suggestions that the high horizontal compressive stresses result from the thermoelastic effects of a convectively cooled upper crustal layer overlying a conductively cooling lithosphere. ¿American Geophysical Union 1990