The relationships between sheet unflatness and nonuniform residual longitudinal bending stresses are investigated. Mathematical analysis shows that edge and center waviness of a short sheet sample may be caused by nonuniform residual bending stresses instead of differential longitudinal strains across the width of the sheet. The latter has often been thought as the only reason for edge and center waviness in sheets. In an infinitely long sheet, or in the inspection zone of a continuous leveling line, the nonuniform residual bending stresses manifest themselves as nonuniform transverse curvatures. There is no longitudinal waviness associated with the residual bending stresses. Nonuniform residual bending stresses may exist in any leveled sheet, to a certain degree, due to initial unflatness and to the strain hardening properties of the alloy. The present study, therefore, may provide a guideline for determining the flattening capability of a leveler in leveling any given alloy with given initial unflatness.

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