<p>The stress-strain state of long cylindrical shells of supercircle cross-section made of nonlinear elastic orthotropic organoplastic is investigated. To improve the convergence of the variation-difference method, a mixed functional with additionally varied membrane strain is used. It is established that due to physical nonlinearity of the composite, stresses decrease while deflections and strains increase. Dependence of the hoop stresses in the nonlinear elastic shell on the properties of the material in contrast to the linear-elastic shell is revealed.</p>