hydroforming method and apparatus are disclosed for preventing or minimizing thinning of a tubular part during its hydroforming in a die cavity . seal units are employed which each have a docking rod that sealing docks at one end with the tubular part and is counterbalanced or overpowered at an opposite end with the same hydroforming pressure that acts in the tubular part on the docking end so that a hydraulic piston that operates the docking rod need only develop sufficient force to exceed the yield strength of the tubular part to effect its compression between the docking rods and thereby effect the addition of material in the tubular part to the portions of the tubular part being stretched during hydroforming .