Wind energy is one of the most promising and the fastest growing alternative-energy production technologies which have been developed in response to stricter environmental regulations, the depletion of fossil-fuel reserves, and the world's ever-growing energy needs. This form of alternative energy is projected to provide 20% of the US energy needs by 2030. For economic reasons, wind turbines (articulated structures which convert wind energy into electrical energy) are expected to operate, with only regular maintenance, for at least twenty years. However, some key wind-turbine components (especially the gearbox) tend to wear down, malfunction and fail in a significantly shorter time, often three to five years after installation, causing an increase in the wind-energy cost and in the cost of ownership of the wind turbine. Clearly, to overcome this problem, a significant increase in long-term gearbox reliability needs to be achieved. While purely empirical efforts aimed at identifying shortcomings in the current design of the gearboxes are of critical importance, the use of advanced computational methods engineering analyses can also be highly beneficial. The present work demonstrates the use of the finite element analysis in modeling and elucidating the root cause of one of the gear failure modes (i.e. toothbending fatigue) under a variety of normal operating and extreme wind-loading conditions.