A method and apparatus are described for the automatic gauging of engineering components. The apparatus includes a clamp for holding a component to be gauged, probes for scanning a surface of the component, drives to provide relative motion between the component and the probes in three mutually perpendicular axes, measuring transducers associated with the drives and the probes to generate signals to measure the degree of movement between the component and the probes, computer memory for storing data relating to a reference profile having dimensions which it is desired to achieve, computer apparatus for comparing signals generated by the measuring transducers with the corresponding signals in the memory, computer apparatus for calculating any error between the stored data and signals generated by the measuring transducers to stack the component to maximize desired coincidence between the dimensions of the reference profile and the actual component. The method and apparatus are described with reference to the gauging of components having aerofoils.