A study on shape memory alloy materials as vibration dampers is reported. An important component is the strain rate-dependent and temperature-dependent constitutive behavior of shape memory alloy, 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 loop size of shape memory alloy 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 shape memory alloy dampers is compared to the same beam with conventional dampers. Parametric studies reveal the superior performance of the shape memory alloy over the conventional dampers even at the resonance frequency of the beam-damper system. An important behavior of the shape memory alloy dampers is discovered, in that they absorb energy from the fundamental and higher vibration modes. In contrast, the conventional dampers transfer energy to higher modes. For the same beam control, the stiffness requirement for the shape memory alloy dampers is significantly less than that of the conventional dampers. Response quantities of interest show improved performance of the shape memory alloy over the conventional dampers under varying excitation intensity, frequency, temperature, and strain rate.