A method of manufacturing a metallic can body that is shaped distinctively in order to enhance its visual presentation to consumers includes, in one embodiment, steps of providing a can body blank that has a sidewall that is of a substantially constant diameter; providing a mold unit that has at least one mold wall that defines a mold cavity that is shaped generally like the can body blank, the mold wall having a pattern formed therein that corresponds to a desired final shape of the can body; positioning the can body blank within the mold cavity; and supplying a pressurized fluid into the mold cavity so that the can body blank is forced by pressure against the mold wall, causing the can body blank to assume the desired final shape of the can body. A second embodiment includes steps of radially deforming the can body blank in selected areas by selected amounts to achieve an intermediate can body that is radially modified, but is still symmetrical about its axis; and superimposing a preselected pattern of mechanical deformations that have an axial component onto the intermediate can body. Related systems and processes are also disclosed.