The shear line, during the orthogonal boring operation, was found to be a circular are extending from the tip of the tool and separating the uncut workpiece from the newly formed chip. Its orientation with respect to the cutting tool was prescribed in this paper, by the condition that the element within the chip, at the base of the tool, did not exceed the yield point of the material as the cutting force was transferred from the tool to the shear line. Under these conditions, a shear-angle relationship, an expression for machining force, and an expression for the chip-thickness ratio were derived for orthogonal boring. It was found, by examining these equations, that as the internal radius of the workpiece increases, the shear angle increases and the machining force decreases, whenever a given depth of cut is taken under identical machining conditions. At the same time, the chip-thickness ratio increases for small friction angles, and decreases for large friction angles. As the internal radius of the workpiece increases, the analytical expressions approach the corresponding equations found for the orthogonal planing operation.