A study on shape memory alloy (SMA) materials as vibration dampers is reported. An important component is the strain rate and temperature dependent constitutive behavior of SMA, which can significantly change its energy dissipation capacity under cyclic loading. The constitutive model used accounts for the thermo-mechanical, strain rate dependent behavior and phase transformation. With increasing structural flexibility the hysteretic loops size of SMA dampers increases due to increasing strain rates, thus further decreasing the response of the structure to cyclic excitation. The structure examined is a beam and its behavior with SMA dampers is compared to the same beam with conventional dampers. Parametric studies reveal the superior performance of the SMA over the conventional dampers even at the resonance frequency of the beam-damper system. An important behavior of the SMA dampers is discovered, in that they absorb energy from the fundamental and from higher vibration modes. In contrast the conventional dampers transfers energy to higher modes. For the same beam control, the stiffness requirement for the SMA dampers is significantly less than that of the conventional dampers. Response quantities of interest show improved performance of the SMA over the conventional dampers under varying excitation intensity, frequency, temperature, and strain rate.