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The article considers the stability of an eccentrically-compressed I-beam rod under the combined action of axial force, bending moment and bimoment. The theoretical analysis of stability is carried out and the dependences of the bearing capacity for such rods are obtained, taking into account the constrained torsion (warping). Theoretical and numerical calculations of eccentrically-compressed cantilever rods of various flexibilities are discussed. The numerical calculations are performed taking into account geometric and physical nonlinearities. The elastic-plastic properties of steel are realized using a unified diagram of the work of steel class C245. The bearing capacity is estimated, which is obtained in three ways: theoretically, numerically (calculations using the Femap with NX Nastran computing complex) and using the normative methodology for calculating eccentrically-compressed rods. Accordingly, the results of a comparative analysis of I-beam stability obtained by these methods are presented. Therefore, it is concluded that ignoring stresses during constrained torsion leads to significant errors in determining the load capacity on an eccentrically-compressed twisted thin-walled rod of an open profile section. [ABSTRACT FROM AUTHOR]