Recently, there have been several instances that the nuclear power plants were shut down due to the mechanical faults in the main transformer of the plants. These mechanical faults are primarily originated from the electromagnetically induced mechanical vibrations. Magnetostriction is identified to be the main cause of the mechanical vibration after analyzing the vibration data of the main transformers in nuclear power plants. In this study, we derived a mathematical model of the magnetostriction based on the Jiles-Atherton hysteresis model. The validity of the model is checked by matching the simulations with the experimental observations. The magnetostriction model used in this study will be the first step toward developing a design tool far the transformers that have minimal mechanical vibrations and are robust to mechanical faults.