This study uses the pseudoelastic properties of Ni–Ti shape memory alloy wires for attenuation of the seismic response of a steel structure and evaluates its effectiveness and applicability in seismic response control. In this paper, shake table tests, carried out on a model of a steel structure with and without wire-based shape memory alloy dampers, are discussed in detail. Shake table tests, comprised of free vibration tests and spectrum compatible time history tests, were carried out. The former were used for the evaluation of the frequency and damping, and the later were used to prove the efficacy of the shape memory alloy dampers. Further analytical simulations are carried out using detailed time history analysis utilizing a thermomechanical model of an SMA and taking into account the residual martensite accumulation, which is irreversibly due to cyclic forward/reverse martensitic transformation. Moreover, a simple iterative response spectrum (IRS) method with equivalent damping and stiffness is also used to evaluate the response of the structure with SMA dampers, and it is proved that the method can be conservatively used by designers.