A workpiece holding device for workpieces to be machined on multiple sides, wherein the workpiece can be held, between a first workpiece holder (104, 106), which is operatively connected to at least one supporting spindle of the workpiece holding device and is rotatable about a first axis, and at least one second workpiece holder, which is operatively connected to at least one drive spindle of the workpiece holding device and is rotatable about the first axis, axially and radially with respect to the first axis and by a frictional connection by means of a clamping force which can be built up in the manner of a vice in the axial direction of the first axis between the first workpiece holder (104, 106) and the second workpiece holder and which acts on opposite sides of the workpiece, wherein the first workpiece holder has at least one first clamping piece (104, 106) having a first flat clamping surface that faces the second workpiece holder and/or the workpiece, and the second workpiece holder has at least one second clamping piece having a second flat clamping surface that faces the first workpiece holder (104, 106) and/or the workpiece, wherein the first clamping piece (104, 106) and/or the second clamping piece have/has a multi-part structure, wherein a first clamping piece part of the particular clamping piece is movable relative to the second clamping piece part of the clamping piece in such a way that a first angle (α') between the first axis and the normal direction of the first clamping surface and/or a second angle between the first axis and the normal direction of the second clamping surface can be changed, wherein the first clamping piece part is in contact with at least one second contact surface of the second clamping piece part in the region of at least one first contact surface of the first clamping piece part, the first axis extending through the center of gravity of the first contact surface and/or the center of gravity of the second contact surface, wherein the first contact surface is smaller than a first surface of the first clamping piece part that faces the second clamping piece part, and/or the second contact surface is smaller than a second surface of the second clamping piece part that faces the first clamping piece part, wherein furthermore the first clamping piece part and the second clamping piece part are interconnected for conjoint rotation by means of at least one bearing (115, 114). the first clamping piece part is in contact with at least one second contact surface of the second clamping piece part in the region of at least one first contact surface of the first clamping piece part, the first axis extending through the center of gravity of the first contact surface and/or the center of gravity of the second contact surface, wherein the first contact surface is smaller than a first surface of the first clamping piece part that faces the second clamping piece part, and/or the second contact surface is smaller than a second surface of the second clamping piece part that faces the first clamping piece part, wherein furthermore the first clamping piece part and the second clamping piece part are interconnected for conjoint rotation by means of at least one bearing (115, 114).