Process industries are becoming increasingly reliant on electrical power for reasons of efficiency and sustainability. A large industrial site typically has its own power management system to distribute electricity to the process and to manage electrical contingencies such as partial loss of supply. Recent work has illustrated more flexible alternatives to load shedding whereby an industrial process plant can continue to operate at a lower level making use of available electrical power. This paper presents a way for achieving such flexibility in a Liquefied Natural Gas (LNG) plant. It analyzes the consequences for production of varying the consumed power, and assesses the maximum flexibility within the feasible operating envelope of the process. The study has been conducted by modeling and simulation of an LNG plant using the Linde process with three refrigeration cycles. The results also show the relationships between electrical power consumption and production in terms of production rate and product characteristics. They also show that the vapour-liquid equilibrium plays a crucial role in establishing the operating points and setting the boundaries in which the process has to work. Thus, through the assessment and simulation of an LNG plant, this work demonstrates that flexible operation has benefits over alternatives. It achieves more operating points and therefore adds more flexibility.