Abstract <p>One of the peculiarities of bending tests of polymer fibrous composites is the need to use cylindrical supports of significant radius to avoid indentation and “nipping” of a sample with low transverse strength. In the refined formulation, a number of effects of the use of cylindrical supports are considered, the influence of which is strictly estimated by expansions in small parameters. The limits of deflection, sample sizes, and support radii are established, when, with a given accuracy, the specified effects can be neglected when determining Young’s modulus and the ultimate strength for normal and shear stresses. It is shown that when finding the interlayer shear modulus, the error that occurs when sample rolls off the supports can be significant; therefore, for the described method, the radius of the supports must be taken into account.</p>