A method of manufacturing an axisymmetric cup with necked edges from an aluminum flat sheet metal by the numerical controlled spinning technique is presented. The first step entails forming a cup-shaped blank along the surface of a die from a flat circular sheet metal by numerical control spinning. The second step entails necking the opening edge of the cup-shaped blank without a die. Suitable conditions for the spinning processes without causing any defects, such as wall fractures and wrinkling, are sought and examined. The process conditions, which include the roll path configuration, the feed velocity of the roll and the revolution speed of the spinning machine spindle, are optimized for successful production. The findings confirm that the numerical controlled necking technique without a die enables us to manufacture necked cups with adequate accuracy and to use the data in the manufacture of other similar products.