Apparatus for detecting faults in inherent flatness in a moving stretched strip, comprising a deflector roll in the form of a cylinder covered by a thin casing. Cavities are machined in the cylinder and arranged on a helix traced on the roll. Each cavity contains a displacement detector whose moving part in contact with the inner surface of the thin casing moves in the radial direction of the roll under the action of the stresses exerted by the sheet. The detectors have a primary winding and a secondary winding through which passes a core, solid with the moving part of the detector. The apparatus includes an optical encoding system for marking the angular position of the roll and a programming apparatus for sending a pulse of current to the primary windings of the detectors once under load and once not under load. A collector and processor for the emitted signals allow calculation of the values proportional to the tension in the strip, along its width. The invention may be used, for example, for monitoring the inherent flatness of thin, cold-rolled sheets.