Buckling Restrained Braced Frame (BRBF) is one of the earthquake resisting system. In this system braces yield in tension and compression without buckling. One of the drawback of conventional BRBF with steel core is residual displacement in frames that are equipped with BRB at the end of earthquakes. for solution of this problem , in this paper BRB is used in the frames with Shape Memory Alloy (SMA) core because of stess-strian diagram of SMA shows small residual stain during cyclic loading. for evaluation of BRB with SMA core, 4 and 8 story 2D frames are selected and equipped with BRB that has steel core and BRB that has SMA core. Frames has been analyzed under Nonlinear Time History with three Earthquake Records. Assessment of results reveal that residual drifts of  BRB frames with SMA core are decrease respect to BRB frames with steel core. Evaluation of  the rest parameters like maximum lateral story displacement, maximum story drift ratio and maximum story shear shows that BRB frames with steel core have better responses respect to BRB frames with SMA core in most cases.