An apparatus is provided for checking the shape of a part having a portion which is a cylinder of revolution around an axis and a reference end face. The apparatus includes a base and a support arrangement mounted on the base for receiving the cylinder portion and comprising two V-shaped pieces. A positioning arrangement is provided for positioning the part axially with respect to the reference end face. A mechanism is provided for driving the part in rotation about the axis. The positioning arrangement comprises a rectilinear portion with an hemispheric end providing an abutment for the end face. The rectilinear portion is mounted slidingly on the base along a direction which forms, with respect to the axis, an angle corresponding to the half of the angle of the V-shaped pieces. An adjustment means is provided for adjusting the position of the rectilinear portion in a manner which maintains the abutment point of the hemispheric end with the end face on the axis.