In this note, regional input-to-state stability (ISS) is introduced and studied in order to analyze the domain of attraction of nonlinear constrained systems with disturbances. ISS is derived by means of a non smooth ISS-Lyapunov function with an upper bound guaranteed only in a sub-region of the domain of attraction. These results are used to study the ISS properties of nonlinear model predictive control (MPC) algorithms.