A new arc consistent viscous-spring artificial boundary (ACVAB) was proposed by changing a traditional flat artificial boundary based on the theory of viscous-spring artificial boundaries. Through examples, the concept underpinning the establishment, and specific setting of, the boundary in the finite element software were described. Through comparison with other commonly used artificial boundaries in an example for near-field wave analysis using the two-dimensional (2-d) half-space model, the reliability of the ACVAB was verified. Furthermore, the ACVAB was used in the numerical analysis of the effects of an earthquake of underground structures. The results were compared with shaking-table test results on underground structures. On this basis, the applicability of the ACVAB to a numerical model of the seismic response of underground structures was evaluated. The results show that the boundary is superior to common viscous-spring boundaries in terms of accuracy and stability, and therefore it can be used to evaluate radiation damping effects of seismic response of underground structures and is easier to use.