coupling procedure of finite element (FE) and scaled boundary finite element (SBFE) is presented for three-dimensional (3D) dynamic analysis of unbounded soil-structure interaction in the time domain. The procedure is implemented with the following efficient techniques: (1) Based on the concepts of linear system theory, the acceleration unit-impulse response matrix of the unbounded soil calculated by the SBFE method is converted into a group of time-independent matrices; thus, the time history of the unit-impulse response function of the unbounded medium can be replaced by an equivalent state-variable description. (2) The interaction forces between the unbounded soil and the structure are evaluated by a system of linear equations instead of time-consuming convolution integrals. (3) Since only the partial information of the unit-impulse response function is sufficient to capture the main character of the unbounded medium and the history of response function can be truncated at the cut-off time tc, the computational effort spent in the SBFE method can be further reduced. In addition, the accuracy of the procedure can be controlled with prescribed parameters, thus the main advantage of the SBFE method as a highly accurate procedure is retained. Three numerical examples of foundation response demonstrate that good agreement can be achieved when compared with previous results, and high efficiency is also evident compared with the direct convolution integral method. Copyright