A measuring device for hollow cylindrical surfaces, such as bores and the like, comprises a housing to be fixed in the bore by clamps, a measuring arm rotatable by a first step motor, a measuring head axially movable along the measuring arm substantially parallel to the axis of the bore surface by a second step motor and a sensor incorporated in the measuring head and radially movable relative to the measuring head against the force of a leaf spring in contact with the bore surface. The leaf spring supports strain gauges, the output signals of which are representative of the radial or transverse paths of the sensor and thereby for the shape of the bore surface to be measured.