In this paper a wave absorption control of one-dimensional flexible systems such as ropes and beams near boundary is treated. Those systems are approximated by finite difference method. The finite difference equation of motion of the end element influenced by the boundary condition is compensated to be the same as an inner element free from the boundary condition with control for the propagating characteristic solution obtained from the equation of motion of an inner element. As the control law has an irrational function, control filter is constructed by using polynomial curve fitting for the rope system. We confirmed the effectiveness of the wave controller for the running rope by both frequency domain response and time domain simulation as the non-running rope in the previous paper. Beams are also wave controlled by compensating the finite difference equation of motion of the end elements. We confirmed the effectiveness of wave control law for beams by the frequency domain response and the time domain simulation using an imaginary propagating system.