Stability tests of a thin-walled composite structure with a closed section are presented in this paper. The purpose of this paper is to conduct preliminary studies in the context of numerical simulations of critical and slightly post-buckling states. The tests were conducted based only on numerical simulations by the finite element method. Numerical simulations were conducted using ABAQUS software, which allowed to determine the values of critical loads and their corresponding buckling forms. The influence of layer arrangement on the stability of the structure was studied. Carbon-epoxy laminate (CEL) was used in the tests. It is shown that there are composite lay-ups that show more than 1.3 times higher stiffness than the other cases. The paper demonstrates the dependence of the influence of the arrangement of layers on the stability of the structure, which will provide the basis for planned experimental studies (the results require experimental verification, which will be carried out in subsequent studies).