Abstract: The multi-transmitting boundary is a local artificial boundary widely used in numerical simulation of the near-field wave motion in infinite media. But like other artificial boundaries, the multi-transmitting boundary has the instability of numerical simulation. The measure is studied for eliminating the instability of the transmitting boundary by means of adding visco-elastic elements in the artificial boundary area. In the measure, the spring-damper elements are emplaced at the finite element nodes next to the artificial boundary in the artificial boundary area. Validity of the suggested measure is tested by numerical analysis. The results show that the proposed measure is effective to solve the drift instability of multi-transmitting boundary, which is valid for eliminating the drift instability but no visible effects on the high-frequency instability .