A method for calculating the power demand of the hoist motor in rubber-tired gantry (RTG) cranes with nonparallel cables has been developed to measure the energy consumption in a typical lift cycle. From measurements taken at the Port of Felixstowe, it has been observed that the peculiar geometrical characteristics of the hoisting mechanism cause the power demand to increase with the container height in constant rotor speed conditions. The change in the angle of the hoisting ropes causes an increase in torque load and power consumption. By using information extracted from the crane’s geometry, it has been possible to calculate the potential energy increase given the weight and vertical position of the container. The load torque on the hoist motor and the vertical speed of the mass have also been calculated, allowing for the modeling of the hoist motor power consumption when lifting containers with constant rotational speed. The proposed model has been compared to a constant power demand approximation, showing a higher accuracy for masses below 40 t.