In Incremental Sheet Forming (ISF) of metal sheets, it is desirable to develop a quick method to predict the mechanical behaviour during forming, and ultimately, to optimise the process. The aim of this paper is to propose a Rapid Kinematic Method (RKM) for a quick update of the positions of the material points in two-point Incremental Sheet Forming (TPIF) of metal sheets. Based on this method, the strain and thickness distributions in the part can be determined and its tendency to fail assessed. The developed RKM is used to simulate single-stage and three-stage ISF of an ellipsoidal shape made of thin aluminium sheets, and the RKM predictions are compared with Finite Element Analysis simulations and experiments. The change in the deformation mechanism introduced by multi-staging has been carefully examined and a strategy for enhancing the sheet formability by structural means identified. The RKM presented here is applicable to parts of general shapes and the updated positions of the material points during ISF thus established can be used as an initial guess for a more rigorous model of mechanics.