Abstract: To satisfy practical requirements for dynamic analysis of engineering structures, accuracy and efficiency have played key roles in the evaluation of interaction forces of unbounded soil in the time domain. Based on the idea that the Damping Solvent Extraction Method (DSEM) simulates the dynamic characteristics of an unbounded soil, a Damping Solvent Stepwise Extraction Method (DSSEM) is proposed by first applying relatively larger artificial damping in the bounded soil and then employing a stepwise extraction process. In essence, the introduced artificial damping is divided into smaller parts to assure the convergence and then extracted step by step, which can simultaneously decrease two sources of error in the implementation of DSEM. Also, the corresponding numerical implementation of the procedure in the time domain is given within the framework of finite elements. This method provides a more efficient and accurate way to calculate the interaction forces of the unbounded soil due to the fluctuation energy of reflected waves and the undesirable effect of artificial damping are completely removed as much as possible. Additionally, the proposed method is applicable to practical engineering with an irregular soil domain, and provides the selection of the artificial damping without depending on the domain size of bounded soil. A typical 3-D strip foundation with rectangular cross-section embedded in half-space under transient excitation is analyzed as verfication. The numerical results are compared with the solution obtained by analytical formula, DSEM, and visco-elastic boundary model. It is shown that the proposed method exhibits good accuracy and efficiency. In the meantime, dynamic analysis of an irregular soil domain model is also presented to demonstrate the engineering capabilities of the method.