Mechanical stress acting in the Earth`s crust is a fundamental property that has a wide range of geophysical applications, from tectonic movements to energy production. The orientation of maximum horizontal compressive stress, SHmax can be estimated by inverting earthquake source mechanisms and directly from borehole-based measurements, but large regions of the continents have few or no observations. Available observations often represent a variety of length scales and depths, and can be difficult to reconcile. Here we present a new approach to determine SHmax by measuring stress induced anisotropy of nonlinear susceptibility. We observe that nonlinear susceptibility is azimuthally dependent in the Earth and maximum when parallel to SHmax, as predicted by laboratory experiments. Our measurements use empirical Green’s functions that are applicable for different temporal and spatial scales. The method can quantify the orientation of SHmax in regions where no measurements exist today.