This paper presents a new methodology for deformable object modelling by drawing an analogy between cellular neural network (CNN) and elastic deformation. The potential energy stored in an elastic body as a result of a deformation caused by an external force is propagated among mass points by the non-linear CNN activity. An improved CNN model is developed for propagating the energy generated by the external force on the object surface in the natural manner of Poisson equation. The proposed methodology models non-linear materials with nonlinear CNN rather than geometric non-linearity in the most existing deformation methods. It can not only deal with large-range deformations, but it can also accommodate isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive constants.