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In this paper, a concave-shaped unit composed of two thin-walled beams with cantilever boundary conditions is designed and fabricated. Forces are introduced through the two cantilever ends of the beams whose constraints are hinged joints to get a bi-stable axial or lateral buckled unit. Initial buckling deformations of the concave-shaped units are analyzed theoretically and numerically. Experimental and numerical methods are used to investigate the post-buckling deformations and snap-through behaviors, when the concave-shaped units are axial buckled or lateral buckled. In the case of completing downwards and upwards snapping processes, there is a hysteresis loop in the force–displacement curve for the bi-stable lateral buckled unit, while is not for the bi-stable axial buckled unit. Finally, the influence of transverse displacements and dimension parameters on the snap-through behaviors of the bi-stable lateral buckled units is studied by the simulation method. • A bi-stable lateral buckled unit is designed and fabricated. • There are two symmetric modes for the initial buckled concave-shaped unit. • Post-buckling and snap-through behaviors of the bi-stable units are investigated. • The energy dissipation capacities are influenced by beams parameters. • The assembly bi-stable units are good candidates for energy-related applications. [ABSTRACT FROM AUTHOR]