The damping capacities of Ti 50 Ni 50¹x Cu x SMAs with x = 0³20 at% were measured by DMA under temperature, strain and frequency sweep tests. The tan ¤ value exhibited at B2¼B19 transformation is significantly higher than that at B2¼B19A transformation under temperature/strain sweep tests. In the strain sweep test, the tan ¤ value decreases as the frequency increases, but it increases as the applied strain increases. The tan ¤ curves of the strain sweep tests can be fitted by tan ¤ = K¾ n with n values being close to the friction type model. Adding Cu enhances the tan ¤ values of both B19 martensite and B2¼B19 transformation in 0.1³10 Hz, but that of B19A martensite is enhanced only at 10 Hz. From 0.1 Hz to 1 Hz, the decrement of the tan ¤ value in IF I term is greater than that in IF PT term for SMA with x ² 5 at%. In the frequency sweep test, the tan ¤ value increases as the x value increases under the same applied frequency, no matter whether the martensite is B19A or B19.