Structural instability, in particular postbuckling resulted in predefined constraints, has been performing advantages in many applications given their promising mechanical characteristics. However, inadequate studies have been conducted to effectively control and tune the postbuckling behavior of bilaterally constrained nonuniform beams. This study develops postbuckling systems comprised of multiple nonuniform beams subjected to bilateral confinements. Theoretical model is developed using Euler-Bernoulli theory and small deformation assumptions to predict postbuckling response of the beam systems under quasi-static axial loading. To locate the minimum energy path of the deformed beam system, the minimization problem of total potential energies of the bi-walled beam systems is solved by Nelder-Mead algorithm. Snap-through transitions of buckled systems are shown by drops in the response curves. To validate the developed model with existing models in literature, the model was simplified to account for single uniform beam under displacement control. The proposed model is experimentally and numerically validated, and satisfactory agreements are obtained. Parametric studies are carried out to investigate the influence of varying the geometric parameters (i.e., length, thickness) of the nonuniform beams on the tunable systems. Using the presented theoretical model, the postbuckling events can be accurately controlled by the geometry properties of the nonuniform beams.