Undervoltage load shedding (UVLS) is the last resort against voltage instability in critical situations. Here, the UVLS scheme is formulated as a mixed integer programming (MIP) model. The aim of the proposed UVLS model is to provide a predetermined value of loading margin with minimum amount of load shed. The full non-linear AC power flow equations are linearised using a piecewise linear technique. The proposed linear AC power flow is then integrated into the UVLS problem. A ZIP load model is utilised to demonstrate the fulfilment of the MIP-based UVLS model under non-linear static loads. The efficacy of the developed linear AC power flow is verified under different operational conditions and contingencies. The results of the proposed MIP-based UVLS model are compared with the original non-linear programming UVLS formulation. To verify the performance of the developed load shedding strategy, the proposed MIP-based UVLS model is implemented in IEEE 14-bus and IEEE 118-bus test systems.