Abstract The paper proposes a class of tunable metamaterials that use inclined beams to achieve instability in a rigid system. Three different beam tilt angles, 25°, 45°, and 60°, are evaluated in the form of unit cells using quasi-static compression tests and numerical simulations. Snap-through behavirous are characterised by structural stiffness and buckling load. Periodic and gradient structures are assembled and analysed by arranging the unit cells in rows and columns. Size effect analyses and parametric studies are carried out on various unit-cell arrangements and different beam angles. The proposed metamaterials are manufactured through fused filament fabrication 3D printing technology with a composite material, onyx. The results from experiments, finite element analysis, and analytical models are compared and evaluated. The structural stiffness and buckling load are shown to be positively related to the inclination angle of the tilted beams. The number of rows of unit cells governs the nonlinear mechanical response (number of snap-throughs) of multiple-layered structures. By increasing the number of rows and columns of unit cells, which are less prone to manufacturing defects, the reliability and repeatability of the structural properties of periodic/gradient structures could be improved. A design plot is also provided to predict and tune the snap-through behaviour of multiple-layered structures via beam angles and unit-cell arrangements.