The concept of the critical path has been widely discussed in many areas of computer engineering such as parallel and distributed programs, a computer circuit, and a directed acyclic graph. The critical path analyzes in a workflow can allow us to utilize it in many workflow issues, especially workflow resource management and workflow time management. In this paper, we first describe our workflow model using the workflow queuing network. Then, we propose a method to systematically determine the critical path under the workflow model, and give an overall example that shows how our method works. In addition, several experiments are made to evaluate the accuracy of the critical path found. (C) 2002 Elsevier Science B.V. All rights reserved.