Unsymmetric composite laminates exhibit two stable configurations at room temperature after being cured at elevated temperature. Bistability of cross-ply laminates is due to the presence of residual strains imparted during the curing process. A simple snap-through process can be used to switch from one stable shape to another. The amount of snap-through force required for attaining the other stable shape depends on the total strain energy of the laminate in the first cured shape. Bistable shapes of the conventional square laminates are in the same energy level, which means the stable configurations are equally stable and results in equal snap-through and snap-back forces. By tailoring the energy levels of stable shapes, snap-through and snap-back forces can be varied. From various studies in the past, it is observed that bistable laminates have enormous potential for morphing applications. In some of the practical applications, one may require stable shapes at different energy levels, with unequal snap-through and snap-back energies for the shape transition. This study aims to tailor the energy levels of bistable shapes of the square laminate by varying the thickness of individual layers in the considered [0/90] square laminates. A detailed parametric study is performed in commercially available finite element software. It is concluded from the study that individual lamina thickness has a noticeable influence on the bistability of cross-ply laminates. © Published under licence by IOP Publishing Ltd.