Abstract: An efficient and accurate erosion contact algorithm is essential for numerical simulation of impact dynamics problems, such as projectile perforation/penetration, high velocity contact, etc. Also,it is one of the most crucial algorithms of the explicit finite element code. In this paper one accurate and robust erosion contact searching algorithm was developed based on the node-to-segment discrete modeling. The ambiguity of contact between slave node and potential contacting master segments was resolved by introducing one history variable together with the contact strength conception. As a result, the slave node-master segment pair and the corresponding contact direction is determined accurately. In contact point computation, one kind of non-iterative algorithm was established, to improve the stability of erosion contact algorithm. All the algorithms were implemented based on explicit finite element code PANDA-Impact, and the effectiveness and robustness were verified by typical numerical examples. The simulation results show the proposed algorithms can be used to simulate complex engineering problems with high accuracy.