Computer simulation of back reflection Laue patterns now provides the means to plot Laue patterns for any crystal system in any orientation. This capability makes it possible to determine, rapidly and accurately, the orientation of single crystals and large grains in polycrystalline materials even in cases where little or no symmetry is displayed in the Laue photograph. A set of standard Laue patterns is first simulated to cover the stereographic triangle of the crystal being studied. The Laue photograph obtained from the crystal, or grain, is compared with the set of simulated Laue patterns. The pattern most similar to the photograph is used to determine the (HKL) values of three Laue spots. The (HKL) values of these spots and half their angular separations from the x-ray beam, along with the lattice constants, are used by a computer program to calculate the (HKL) value of the crystallographic plane perpendicular to the x-ray beam. A simulated Laue pattern can now be obtained in exactly the same orientation and it can be drawn directly to the scale of the Laue photograph. Thus the validity of the orientation can be easily verified by direct comparison. The (HKL) value of the crystallographic plane perpendicular to the x-ray beam can also be used to plot a stereographic projection of the crystal poles. Therefore, the complete orientation of the crystal can be determined.