A method and apparatus for receiving a tire, especially for checking the concentricity of a pneumatic vehicle tire that during operation has its bead portions mounted on the radially inner periphery of a wheel rim. A test rim is provided that comprises two axially movable rim ring sections that in turn are provided with pivotable rim flange segments toward which cooperating parts are axially movable from beyond the tire. The bead zones of the trapezoidally mounted tire are engaged by the cooperating parts and are brought into the rim-setting position. The pivotable rim flange segments are swung radially inwardly, so that the bead portions are held between the cooperating parts and the rim ring sections. The bead seat is sealed by sealing lips.