This paper presents a new methodology for the deformation of soft objects 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 nonlinear CNN activities. The novelty of the methodology is that soft object deformation is carried out from the perspective of energy propagation, and nonlinear material properties are modelled with nonlinear CNNs, rather than geometric nonlinearity as in most of the existing deformation methods. Integration with a haptic device has been achieved to simulate soft object deformation with force feedback. The proposed methodology not only predicts the typical behaviors of living tissues, but also easily accommodates isotropic, anisotropic and inhomogeneous materials, and local and large-range deformation.