A method of obtaining admissible velocity fields without velocity discontinuities is described, and applied to plane-strain extrusion, tube extrusion, and axisymmetric piercing. In plane-strain extrusion, the flow lines, grid distortions, and extrusion pressures were obtained and the values were compared with those found in previous solutions. For tube extrusion and axisymmetric piercing, the solutions are presented as examples in terms of flow lines and velocity component distributions; these solutions await experimental confirmation.

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