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This paper concentrates on the vibration control problem of a flexible string system and a flexible Euler-Bernoulli beam system for considering full state output constraints, i.e., deflection and speed constraints. For either system, a boundary control law is developed based on a barrier Lyapunov function. By employing the control scheme, the deflection and speed are limited into desirable regions. With the help of a rigorous unique solution proof for the time derivative of the barrier Lyapunov function, the asymptotic stability of the considered system is achieved via LaSalle's Invariance Principle. Finally, numerical simulations are provided to verify the control performances of the proposed controls.