This paper presents a new methodology for the deformation of soft objects by drawing an analogy between Poisson equation 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 Poisson equation. An improved Poisson model is developed for propagating the energy generated by the external force in a natural manner. A cellular neural network (CNN) model is established to solve the Poisson model for the real-time requirement of soft object deformation. A haptic virtual reality system has been established for deformation simulation with force feedback. This proposed methodology not only deals with local and large-range deformations, but also accommodates isotropic, anisotropic and inhomogeneous materials by simply modifying constitutive coefficients, as well as predicts the mechanical behaviors of living tissues.