One of the authors (DMS) thanks his colleagues at NIST, Edwin R. Fuller, Jr. and Grady S. White, for their helpful advice and criticisms, as well as Mark D. Vaudin and James A. Warren for their critical review of this manuscript. This work was supported at CMU by the MRSEC program of the National Science Foundation under Award No. DMR-0079996. A sterological method is described for estimating the distribution of grain-boundary types in poly-crystalline materials on the basis of observations from a single planar section. The grain-boundary distribution is expressed in terms of five macroscopically observable parameters that include: three parameters that describe the lattice misorientation across the boundary and two parameters that describe the orientation of the grain-boundary plane normal. The grain-boundary distribution is derived from measurements of grain orientations and the orientations of the lines formed where grain boundaries intersect the plane of observation. Tests of the method on simulated observations illustrate that the distribution of boundaries in a material with cubic symmetry can be reliably determined with about 10 degrees of resolution from the analysis of 5 x 10E4 or more line segements. Furthermore, grain-boundary distributions directly observed from serial sections of a SfTiO3 polycrystal are compared to those resulting from the stereological analysis of a single plane. The comparison shows that the stereological method provides a reasonable estimate of the measured distribution. The differences between the directly observed grain-boundary distribution and that derived from the stereological analysis are consistent with the results from the simulation.