A method for producing a workpiece by electrochemical removal of a starting material, including the method steps of: - embodying a reactor chamber among a thus-far embodied surface of the starting material, a hollow-cylindrical reactor tube, and a tool, located movably guided in the reactor tube; - equipping a side of the tool, opposite the thus-far embodied surface of the starting material and facing toward the starting material to be treated, with a negative form of the workpiece to be produced; - moving the tool, located movably guided in the reactor tube, at a constant spacing from the surface of the starting material, which surface recedes with increasing electrochemical removal, during the electrochemical removal, characterized in that: - at least during the electrochemical removal, negative pressure, relative to an environment outside the reactor chamber, prevails in the reactor chamber; - an electrolyte circulates in a circular motion that includes the reactor chamber, in which circular motion a vapor deposition takes place, once the electrolyte has left the reactor chamber and before the electrolyte is re-delivered to the reactor chamber; and - the negative pressure prevailing in the reactor chamber relative to an environment outside the reactor chamber is established, in the vapor deposition in the circular motion, by withdrawal of a gas phase outside the reactor chamber. including the method steps of: - embodying a reactor chamber among a thus-far embodied surface of the starting material, a hollow-cylindrical reactor tube, and a tool, located movably guided in the reactor tube; - equipping a side of the tool, opposite the thus-far embodied surface of the starting material and facing toward the starting material to be treated, with a negative form of the workpiece to be produced; - moving the tool, located movably guided in the reactor tube, at a constant spacing from the surface of the starting material, which surface recedes with increasing electrochemical removal, during the electrochemical removal, - embodying a reactor chamber among a thus-far embodied surface of the starting material, a hollow-cylindrical reactor tube, and a tool, located movably guided in the reactor tube; - equipping a side of the tool, opposite the thus-far embodied surface of the starting material and facing toward the starting material to be treated, with a negative form of the workpiece to be produced; - moving the tool, located movably guided in the reactor tube, at a constant spacing from the surface of the starting material, which surface recedes with increasing electrochemical removal, during the electrochemical removal, characterized in that: - at least during the electrochemical removal, negative pressure, relative to an environment outside the reactor chamber, prevails in the reactor chamber; - an electrolyte circulates in a circular motion that includes the reactor chamber, in which circular motion a vapor deposition takes place, once the electrolyte has left the reactor chamber and before the electrolyte is re-delivered to the reactor chamber; and - the negative pressure prevailing in the reactor chamber relative to an environment outside the reactor chamber is established, in the vapor deposition in the circular motion, by withdrawal of a gas phase outside the reactor chamber. - at least during the electrochemical removal, negative pressure, relative to an environment outside the reactor chamber, prevails in the reactor chamber; - an electrolyte circulates in a circular motion that includes the reactor chamber, in which circular motion a vapor deposition takes place, once the electrolyte has left the reactor chamber and before the electrolyte is re-delivered to the reactor chamber; and - the negative pressure prevailing in the reactor chamber relative to an environment outside the reactor chamber is established, in the vapor deposition in the circular motion, by withdrawal of a gas phase outside the reactor chamber.