The fault cutting algorithm is important when applying the three-dimensional numerical manifold method to engineering simulation. This paper presents a primary approach to the fault cutting algorithm, including data structures, fault cutting procedures, and some basic computing algorithms. First, the data structures of the physical elements and mathematical covers are proposed as single linked lists and linked list arrays, respectively. This reduces the complexity of the algorithm and increases the efficiency when connecting physical elements to covers. Second, a strategy of recording cutting traces between every two faults to ensure that the model agrees with the actual situation was proposed. This strategy also reduces the complexity and improves the efficiency. Third, the mathematical covers and physical elements are cut with all faults independently to process complete cutting instances in a multiblock form and incomplete cutting instances without forming any new irrational block. Finally, four cutting examples are presented that demonstrate that the proposed fault cutting algorithm is correct and useful. (C) 2016 American Society of Civil Engineers.