This paper demonstrates, theoretically and experimentally, the feasibility of utilizing Shape Memory Alloy (SMA) as an actuator in controlling the flexural vibrations of a flexible cantilevered beam. The shape memory alloy used in this study is merely a straight wire which is made of nickel titanium alloy called Nitinol. Acting as tendons, these SMAs undergo phase transformation, to the austenitic phase, producing significant forces and displacement capabilities as well as low power consumption. This actuator unit is composed of a SMA wire attached to a spring in series. After being set-up with a load cell the transfer functions of the actuator are measured. Considering the uncertainty of the actuator unit performance the H-infinity optimal controllers are designed and installed into the control system. By integrating the thermal and dynamic characteristics of the SMA into beam dynamical model the composite beam-actuators system can now be developed. The robust stability performance of the designed controller is evaluated through vibrational test on the cantilever and the result is shown to be adequately attenuated.