Abstract: A method of finishing two opposite edges (5, 6) of a single workpiece (1) by machining, the machining giving each edge a desired final shape by pressing the workpiece between a pair of tools (7, 8) having shapes (9, 10) complementary to the desired finished shapes for the two edges. According to the invention the complementary shapes (9, 10) of the tools (7, 8) are limited by causing them to correspond solely to the finishing zones (5a, 6a) of the two edges (5, 6), and during the finishing operation per se, the two tools are controlled to move simultaneously in translation (18-20, 19-21). The method is applicable to finishing holes through a high precision workpiece such as used in some jet engines.