The article presents the results of methodological developments aimed at studying the distribution of residual stresses across the thickness of thin-sheet rolled materials. The specimens subject to direct testing are narrow strips cut from the workpiece along and across the rolling direction. The determination of stresses in the specimen is performed by the method of gradually deepening transverse slit. As a registered response, it is proposed to consider the angle of the arising mutual rotation of the end parts of the sample. For its reliable registration, the most optimal non-contact optical methods should be considered: electronic speckle pattern interferometry or digital image correlation. The choice of a specific one is determined by the test conditions. The procedure for interpreting primary experimental information in terms of residual stresses is formulated as an inverse problem of solid mechanics. Two possible mathematical approaches to data processing are considered, taking into account the incorrectness of the problem statement. Stabilization of the solution is achieved, among other things, through the use of a regularization algorithm. The efficiency of the performed developments is demonstrated by the study’s example of stress distributions in specimens of thin-sheet rolled steel — products of the Novolipetsk Metallurgical Plant. It is shown that different approaches to mathematical processing give practically identical results.