A device (10-100) for the localized strain of extruded or drawn bodies, especially containers or bombs (66) provided with a mouth from aluminum or other suitable material, having a cylindrical form, painted and/or lithographed, fed on a grasping means or pliers of a tapering machine for tapering their upper part, comprising: a substantially cylindrical body, having differentiated diameters, wherein a lever (44-110, 110') is provided that bears a counter-mold (90 - 156,156') in touch with the internal lateral surface of containers (66) starting from their mouth; at least a straining tool (64, 64'-150, 150') cooperating with the counter-mold (90-156,156') to obtain at least a raised and/or recessed impression on said containers; supporting (72, 72'-142, 142') and guide (80, 82 - 146,146') means for said at least one straining tool (64, 64'-150, 150'), suitable to lead said straining tool to cooperate with said counter-mold (90,156,156').