Dedicated finite element models are developed to simulate the crossing of a pipeline integral buckle arrestor by a buckle propagating under the quasi-static, steady-state condition. In addition, broad parametric studies are conducted to identify the mechanism governing the arresting performance, which consider the geometric characteristics and material properties of the pipe and arrestor. Based upon the extensive study, the more reasonable empirical design formulas for the crossover pressure and the arresting efficiency are established by means of the partial fitting. Good agreements between the existing experimental results and the predictions demonstrate that the proposed empirical formula and the lower bound envelope line for the arresting efficiency provide a powerful design tool to estimate the arresting performance of such complex structure systems in engineering practices.