The purpose of this work was to develop a method of determining far-field principal stress magnitude and orientation using biaxial stress measurements made in a series of bore holes. Two novel developments were employed: one was a method for relating biaxial measurements from three bore holes to the triaxial principal stress field; the other was a measurement technique that fully defines the biaxial stress field around a bore hole, independent of rock properties. To determine the triaxial principal stress field, a series of simultaneous equations describing biaxial measurements in terms of a random baseline coordinate system was developed. A least squares regression was then utilized to determine the coordinate system's stress field. A Newton-Raphson reduction was subsequently performed to define the orientation and magnitude of the principal stress field. The biaxial stress measurement technique employs two loading mechanisms and ultrasonic crack detection. The biaxial stress field in bore holes with nonhomogeneous and anisotropic rock conditions can be defined. Finally, recommendations are given for the development of a testing apparatus utilizing thin-film piezoelectric substrates to detect ultrasonic shear waves capable of underground biaxial measurements.