Experimental results on the dynamics of a beam constrained by shape memory wires are presented. It is observed that the damping increases significantly when the shape memory wires are stressed such that they lie within the pseudoelastic hysteresis loop. Theoretical models of the inner hysteresis loop are considered, and modal analysis is used to obtain the dynamic response of the system. Simulations of the system using these models give theoretical values of damping which agree well with those observed experimentally. The proposed models of the pseudoelastic hysteresis loop are adequate for providing an estimate of the initial increase of damping due to the use of prestressed shape memory wires in structures. These results demonstrate that pseudoelasticity of shape memory wires can be used to augment passive damping significantly in structural systems.