In this article we investigate a Lyapunov approach to the stability of finite-dimensional 2D systems. We use the behavioural framework and consider a notion of stability following the ideas in Pillai and Shankar [H. Pillai and S. Shankar (1998). A Behavioral Approach to Control of Distributed Systems, SIAM Journal of Control and Optimization, 37, 388-408], Rocha [P. Rocha (2008). Stabilization of Multidimensional Behaviors, Multidimensional Systems and Signal Processing, 19, 273-286], Valcher [M. Valcher (2000). Characteristic Cones and Stability Properties of Two-dimensional Autonomous Behaviors, IEEE Transactions on Circuits and Systems, Part I, CAS-47, 290-302]. We characterise stability in terms of the existence of a (quadratic) Lyapunov function and provide a constructive algorithm for the computation of all such Lyapunov functions.