Multistable shells have been recently proposed as an effective solution to design morphing structures. We describe a class of shallow shells which are bistable after one of their sides, initially curved, is clamped along a flat line. Supposing the shell being assembled as a composite laminate, we show how the anisotropy of the material can influence the multistable behaviour and the robustness of stable configurations. Specifically, we focus on orthotropic laminated shells using the polar method for a complete representation of the anisotropic elastic properties. Two experimental prototypes have been produced and tested to validate our analytical and numerical results.