In this article, mechanics model of SMA center tension from damper is developed. According to the theory of Brinson constitutive model and thermodynamics first law, damper thermodynamics non linear equation has been developed. Dynamics non linear equation of frame structure under operation of SMA damper and its solution have been worked out; the software of seismic response analysis for frame structure and of damper characteristic analysis have been compiled with MATLAB software, and the examples have been computed with it. The result indicates that SMA damper has obvious damp characteristics and it can provide with obvious restraint effect for seismic response of frame structure. Decreasing rate of displacement and velocity on top of frame structure reaches 50 %-60 %. The result is in accordance with other pundits experimentation results, which indicates that the above methods are correct and useful. In this article, mechanics model of SMA center tension from damper is developed. According to the theory of Brinson constitutive model and thermodynamics first law, damper thermodynamics non linear equation has been developed. Dynamics non linear equation of frame structure under operation of SMA damper and the solution has been worked out; the software of seismic response analysis for frame structure and damper characteristics analysis have been compiled with MATLAB software, and the examples have been computed with it. The result indicates that SMA damper has obvious damp characteristics and it can Decreasing rate of displacement and velocity on top of frame structure reaches 50% -60%. The result is in accordance with other pundits experimentation results, which indicates that the above methods are correct and useful