The paper considers the problem of estimating the stress-strain state of a cylindrical pipe section according to measured vertical displacements of a number of cross-sections of the cylinder. The problem is ambiguous, as there are an infinite number of different variants of loading, under the action of which we obtain the same values of displacements at a finite number of the set points of the pipeline. Four variants of such loading from the hard(concentrated load) to soft (continuously distributed according to some rule) are discussed. As a model of a cylindrical pipe section is used the linear theory of thin shells. The method of orthogonal sweep Godunov is used for the numerical solution of the corresponding linear boundary-value problems.