A method of displaying machining shapes in a wire discharge machining apparatus which moves the work relative to a wire electrode, and which horizontally moves a guide by which the wire electrode is stretched to machine the work in a tapered manner. The method comprises a first step which receives a programmed passage (WDP) on the lower surface of the work, thickness of the work, tapered angle alphai of the blocks or either one of position deviation vectors (ui, vi) on the upper and lower surfaces of the work, and data that specified the number n of sectional shapes (S1, S2, ....., Si, .....) formed by cutting the tapered surface on a plane in parallel with the lower surface of the work; a second step for finding a wire electrode passage (WUP) on the upper surface of the work which is not the programmed surface by using the programmed passage (WDP), thickness of the work, and tapered angle or position deviation vector; a third step for finding coordinate values of points (Q1S, Q2S, ....; Q1e, Q2e, ....) of sectional shapes at the ends of the blocks using wire electrode passage data on the upper and lower surfaces of the work, and the number n of sectional shapes; and a fourth step which displays on a display unit the wire electrode passages (WUP, WDP) and sectional shapes (Si) of the tapered surface by using wire electrode passage data on the upper and lower surfaces of the works and coordinate values of points of sectional shapes at the ends of the blocks.