Abstract-One critical task in wind turbine shaft torsional vibration study involves the modeling of a wind turbine and power grid. With a focus on the mechanical rotational system of wind turbine, this article provides a three-mass shaft model upon which one wind turbine to infinite bus model can be developed. The model, based on small-signal stability analysis, is used to study the wind turbine shaft torsional vibration. For this reason, this article concentrates on the union model of stall wind turbine and power grid. The small-signal stability model includes the mechanical system and electrical system. Data for the turbine's blades and shaft as well as electrical generator are given to allow replication of the model in its entirety. Each of the component blocks of the wind turbine and power grid is modeled separately so that one can easily expand and modify the model to simulate variable-speed wind turbines or multi-turbines system to suit their needs. This is then followed by a case study that explains how the small-signal stability model can be used to study wind turbine shaft torsional vibration issues. Results obtained from the case study show that the model performs as expected.