The study analysed a bisymmetric closely-spaced built-up member, pin-supported at both ends. Itwas bipolarly pre-stressed with a displacement (BPCSBM), and loaded with an axial compressive force. Maximum internal gap between the chords was assumed in the section, in which during the stability failure in a classic closely-spaced member, the largest lateral displacements between nodes would potentially occur. As regards the BPCSBM chosen for analysis, the issues of the buckling resistance in the presence of compressive axial load were solved using the energy method, in which the functional minimisation was performed in accordance with the Rayleigh–Ritz algorithm. The problem of BPCSBM stability was also solved using FEM. A spatial shell model was developed. The stability analysis was performed. The analysis resulted in obtaining the buckling load and the member buckling modes. A general conclusion was formulated based on the results obtained: bipolar pre-stressing leads to an increase in buckling resistance of closely-spaced members.