The hydrodynamics of a three-dimensional self-propelled flexible plate in a quiescent flow were simulated using the immersed boundary method. The clamped leading edge of the flexible plate was forced into a prescribed harmonic oscillation in the vertical direction but was free to move in the horizontal direction. Several types of trapezoidal plates were simulated by changing the shape ratio (S = Wt/Wl), where Wt is the trailing edge width and Wl is the leading edge width. The aspect ratio was fixed at AS = (Wl + Wt)/2L = 0.4, where L is the length of the plate. To explore the hydrodynamics of a rectangular plate (S = 1.0), the average cruising speed (ŪC), the input power (P¯), and the swimming efficiency (η) were determined as a function of the flapping frequency (f). The kinematics of the plate, the maximum angle of attack (ϕmax), and the mean effective length (L¯eff) were examined to characterize the hydrodynamics, including the peak-to-peak amplitude (At/A) and the Strouhal number (St=fAt/Ūc). Next, the effect of S on the hydrodynamics was explored for 0.1 ≤ S ≤ 3.0. The swimming efficiency was found to be the highest at S = 0.5. The maximum thrust (Ft,max) of S = 0.5 decreased by 15% compared to that of S = 1.0, and the maximum lateral force (Fl,max) decreased by more than 50%. The velocity field behind the plate and the vortical structures around the plate were visualized. The influence of the tip vortex on the swimming efficiency was examined.