Because of the effects of gravity and/or residual stress, some manufactured mechanical parts, such as sheet metals and skins, often have a significantly different shape in a free-state position as compared to their state-of-use position. These parts are described as compliant, flexible or nonrigid. Expensive specialized fixtures are currently used prior to performing geometrical inspection operations in order to maintain compliant parts in the state-of-use position. This paper introduces an automatic bi-criterion flexible registration method for the dimensional and geometric inspection of such parts. The proposed method deforms the data acquired via a non-contact scanner of a compliant part in a free-state position until it reaches the nominal CAD shape for inspection with conventional Computer-Aided Inspection (CAI) tools. In other words, the method neutralizes the deviations induced in a compliant part by the effects of gravity and residual stress, allowing the acquired data to be treated as if it were obtained from a rigid part, using already available conventional (rigid) CAI tools. A proposed algorithm based on the BOFR-2 (the 2 nd version of a Bi-Objective Flexible Registration algorithm) method is validated against both virtual simulated and experimental real industrial case studies from the aerospace sector. The resulting cost reduction and agility increasing make this fixtureless method well adapted to the requirements of unit-batch production in the context of Industry 4.0.