Test-cases play an important roll for high quality software testing. Inadequate test-cases may cause bugs remaining after testing. Overlapped test-cases lead to increases in testing costs. The paper proposes a test-case generation method with the EIAG (Event InterActions Graph) and the ISTC (Interaction Sequences Testing Criteria). The EIAG represents behavior of concurrent programs. It 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. The ISTC proposed are based on sequences of Interactions. The cooperated paths (copaths) on the EIAG as test-cases satisfying the ISTC are generated. The generated copaths can detect dead (unreachable) statements which concern interactions, and they can find some communication errors and deadlocks in testing. It is, however, necessary to validate feasibility of the generated copaths.