The article is devoted to the mathematical modeling of the nonlinear stress-strain state of the concrete core in the concrete-filled steel tube structures. The paper uses a nonlinear diagram of concrete deformation under compression, which consists of two straight sections. In addition, the increase in the Poisson's ratio with increasing longitudinal deformations is taken into account. The article discusses two types of concrete-filled steel tube structures: the traditional concrete-filled steel tube column and the concrete column in steel tube cage. It is established that when the traditional concrete-filled steel tube column is loaded, the steel tube break contact with concrete core. This is the latent defect in such structures. The concrete column in steel tube cage does not have this defect. Concrete is acted to the three-dimensional compression here. It is concluded that taking into account the nonlinear behavior of concrete leads to the increasing of the calculated load-bearing capacity of the concrete column in the steel tube cage. In addition, change in the Poisson’s ratio of concrete leads to the increasing of the load-bearing capacity too.