This paper presents a new methodology for the 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 autonomous CNN model is developed for propagating the energy generated by the external force on the object surface in the natural manner of heat conduction. A heat flux based method is presented to derive the internal forces from the potential energy distribution established by the CNN. The proposed methodology models non-linear materials with non-linear CNN rather than geometric non-linearity in the most existing deformation methods. It can not only deal with large-range deformations due to the local connectivity of cells and the CNN dynamics, but it can also accommodate both isotropic and anisotropic materials by simply modifying conductivity constants. Examples are presented to demonstrate the efficacy of the proposed methodology.