The problem of viscoplastic dynamic bending layered fiber plates of variable thickness. The original method of integration of the initial-boundary value problem. The comparison of numerical results with the known analytical solution obtained in the framework of rigid-plastic model for isotropic circular plate, shows their good agreement. The effectiveness of this method is demonstrated by calculations of dynamics of inelastic single-layer and three-layer reinforced plates fixed and variable thickness. It is shown that due to the rational profiling and reinforcement plates the maximum value of the residual deflection can be reduced by several times.