The self-sustained flapping of a three-dimensional flexible plate in a uniform viscous flow is numerically simulated with a fictitious domain method. The effects of the various non-dimensional control parameters including the Reynolds number, the density ratio, the dimensionless shear modulus, the length–thickness ratio, and the width–length ratio on the flapping of the plate are investigated. The results show that there exist two flapping modes: symmetrical and asymmetrical flapping about the centerline in the spanwise direction. Near the critical point a decrease in the plate width–length ratio, or the increase in the Reynolds number or the reduced velocity (a combination of the density ratio, the dimensionless shear modulus, and the length–thickness ratio) can make symmetric (or nearly symmetric) flapping become asymmetric. It is found that the flapping amplitude is mainly controlled by the density ratio and the dimensionless elastic modulus, while the frequency by the density ratio and the length–thickness ratio. In addition, the flapping amplitude and frequency are affected significantly by the confinement effect of the computational domain, and normally enhanced as the confinement effect becomes stronger. The effects of the plate width and the mass ratio (i.e., the ratio of the length–thickness and density ratios) on the critical reduced velocities are examined. The results indicate that when the fluid–plate mass ratio (or the plate length–thickness ratio) is relatively small there exist two significantly different critical velocities for the flapping instability, depending on the strength of initial plate deformation, a hysteresis phenomenon. No obvious hysteresis can be observed when the fluid–plate mass ratio (or the plate length–thickness ratio) is large.