Digital Clay represents a new type of 3-D human-computer interface device that enables tactile and haptic interactions. The Digital Clay kinematics structure is computer controlled and can be commanded to acquire a wide variety of desired shapes (shape display), or be deformed by the user in a manner similar to that of real clay (shape editing). The design of the structure went through various modifications where we finally settled on a crust matrix of spherical joint unit cells. After designing the kinematics structure, the next step is predicting the deformation of the crust matrix based upon a handful of inputs. One possible solution for predicting the shape outcome is considering minimizing the potential energy of the system. In this thesis two methods will be introduced. The first method will be an abstract model of the crust where the energy is calculated from a simplified model with one type of angular springs. The second method is the actual manufacturable crust model with two types of angular springs. From the implementation of these two methods, the output will be center-points of the unit cells. From the center-points, one can also calculate the joint angles within each unit cell.