Problems of stress-strain state of a core-strip under the influence of the cross-section and longitudinal running efforts enclosed to longitudinal sides and presented in the form of symmetric and antisymmetric components are considered. In points of cross-section sides such boundary conditions that have allowed finding exact analytical solutions of considered problems at their formulation proceeding from the two-dimensional equations of a flat problem of the theory of elasticity are accepted. Solutions of the same problems with respect to the flat stress-strain state have also been found and taking into account the one-dimensional equations of specified theory of cores based on previous constructed generalized classical model. The analysis we carried out of the found solutions has shown, that the offered generalized classical model has rather high degree of accuracy even for rather short cores at research of their stress-strain state out of zones of regional effects.