Test-cases play an important roll for high quality of software testing. Inadequate test-cases may cause bugs remaining after testing. Overlapped test-cases may do cost increasing.This paper proposes the Event InterActions Graph (EIAG) representing behavior of concurrent programs and the cooperated paths (copaths) on the EIAG as test-cases. The EIAG consists of Event Graphs and Interactions. An Event Graph is a control flow graph of a program unit in a concurrent program. The Interactions represent interactions (synchronizations, communications and waits) between the program units. Copaths can be generated automatically by the algorithms which are presented in this paper. The generated copaths can detect dead (unreachable) statements and find some communication errors in testing. However, it is necessary to validate feasibility of the generated copaths.