Abstract <p>For the application of the standard ply-by-ply method for calculating composite structures, the complete set of a material’s elastic properties must be determined, which involves numerous difficulties. This work examines several methods for approximate estimation of the elastic constants of single plies and symmetric ply pairs of composites, used, in particular, in the manufacture of pressure vessels. The error in reconstructing a material’s elastic constants based on a known higher Young’s modulus is determined. It is shown that, in addition to the degree of anisotropy of the composite, this error is substantially influenced by the scatter of experimental data in the set of properties used for a given class of composites (carbon-fiber (CFRP), glass-fiber (GFRP), or organic-fiber (OFRP), which should be taken into account when performing calculations. These conclusions are illustrated by stress calculations in ply pairs of a composite pressure vessel. Ply-by-ply calculation results using the full set of elastic constants are compared with results obtained using an approximate estimation of elastic constants using invariants of elastic modulus transformation. It is demonstrated that for highly anisotropic composite materials such as carbon-fiber composites, where the modulus along the fibers greatly exceeds other elastic constants, the approximate methods make it possible to perform calculations of composite structures with acceptable accuracy without resorting to cumbersome computational procedures.</p>