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The dynamic structure–unbounded foundation interaction plays an important role in the seismic response of structures. The damping solvent extraction (DSE) method put forward by Wolf and Song has a great advantage of simplicity, with no singular integrals to be evaluated, no fundamental solution required and convolution integrals avoided. However, implementation of DSE in the time domain to large-scale engineering problems is associated with enormous difficulties in evaluating interaction forces on the structure–unbounded foundation interface, because the displacement on the corresponding interface is an unknown vector to be found. Three sets of interrelated large algebraic equations have to be solved simultaneously. To overcome these difficulties, an efficient algorithm is presented, such that the solution procedure can be greatly simplified and computational effort considerably saved. To verify its accuracy, two examples with analytical solutions were investigated, each with a parameter analysis on the domain size and amount of artificial damping. Then with the parameters suggested in the parameter study, the complex frequency–response functions and earthquake time history analysis of Morrow Point dam were presented to demonstrate the applicability and efficiency of DSE approach. Copyright © 2007 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]