In a cup-type or “silk hat”-type wave gear device (1), the rim thickness t of the flexible externally toothed gear (3) thereof satisfies the relations (0.5237Ln(R)−1.32)d≦t≦(0.8728Ln(R)−2.2)d if the reduction ratio R of the wave gear device is less than 80, and (1.5499Ln(R)−5.8099)d≦t≦(2.5832Ln(R)−9.6832)d if the reduction ratio R is equal to or greater than 80, where d is the radial deflection, measured at the position of the major axis of the neutral circle of the rim, in a state in which the flexible externally toothed gear is bent into an elliptical shape. The effective face width L of the external teeth (35) is a value within the range of 21 to 30% of the pitch circle diameter. Such settings make it possible to increase the bottom fatigue strength of the flexible externally toothed gear and improve the load capacity of the wave gear device (1).