Summary: Extinction readings are taken, on a polarizing microscope, for several wave-fronts in a biaxial crystal (more than four wave-fronts are required). With these extinction data, the machine then calculates the directions of the two optic axes and of the three principal axes of the indicatrix, as well as the value of the optic axial angle 2V, using a least-squares successive approximation technique. The programme was written for an IBM 1620 computer.