Unsymmetric composite plates show promise in the fields of morphing structures, robotics, and energy harvesting due to their ability to exhibit bistability and snap-through behaviour. Precise characterisation of their stable states and snap-through behaviour is crucial for design and optimisation, but it is challenging due to their nonlinearity and susceptibility to uncertainties. This paper introduces a computationally efficient analytical model for characterising the force–displacement response of bistable unsymmetric composite plates and its sensitivity to various factors, including gravity, plate imperfections, and uncertainties in lamina properties and the temperature change during manufacturing. FEA and experimental force–displacement curves are obtained to validate the model. The analysis demonstrates that the model is capable of accurately accounting for the influence of gravity and asymmetry resulting from imperfections. To achieve high accuracy, it is necessary to employ sixth or eighth-order models. The sensitivity analysis demonstrates that variations in lamina elastic moduli, transverse thermal expansion coefficient, ply thickness, and manufacturing temperature change have significant influence on the predicted equilibrium states and force–displacement response. Precise characterisation of these properties is critical for accurate design and analysis, as is strict manufacturing control to reduce uncertainties and imperfections and ensure the structure behaves as desired.