We propose a method to estimate stress magnitudes in oceanic plate interiors from focal depths and focal mechanisms. Using a depth-dependent rheology, we show it is possible to estimate the differential stress (&sgr;1--&sgr;3), averaged over some reference lithospheric thickness. The resolving power of the method is investigated by evaluating the effect of uncertainties in parameters that are involved in the analysis. We apply the method to the Central Indian Ocean, where intraplate seismicity is high. From well-studied earthquakes we estimate differential stresses of the order of hundreds of megapascals. This result is consistent with the high level of stress that was found from numerical model calculations by Cloetingh and Wortel (1985, 1986). From the few intraplate events in the Pacific plate, we also estimate differential stresses in this area. ¿ American Geophysical Union 1992