PURPOSE: To provide a process for producing neck-in cans capable of forming tapered neck-in parts having a sufficient diametral reduction rate and excellent strength without generating wrinkles with a smaller number of stages.

CONSTITUTION: First to third stepped parts are formed by first to third metal molds. The second metal mold presses the first step part from inward to prevent buckling and imparts resistance to the descending of the upper mold by energizing of a core, thereby forming the second step part without generating the wrinkles therein. The third metal mold presses the first and second step parts respectively from inward to prevent the buckling and imparts the resistance to the descending of the upper mold by energizing of the core, thereby forming these step parts without generating the wrinkles therein. The first to third stepped parts are then formed flat toward the diametral reducing direction by the fourth metal mold, by which the tapered neck-in part is formed.