A task-type in concurrent programs is a template of task-instances which are dynamically generated in execution of the programs. The number of the generated task-instances may not be statically determined. Therefore, test-cases generated by our previously proposed method may not be realized in execution of the programs. This paper proposes an enhanced test-case generation method. Concurrent programs are classified into four kinds under two viewpoints: whether the number of task-instances generated from a task-type can be determined statically or dynamically, and whether or not the task-instances communicate with each other. The enhanced method uses a modified Event InterActions Graph(EIAG). The EIAG consists of Event Graphs and Interactions. An Event Graph is an abstract control flow graph of a program unit. The Interactions represent interactions between the units. Because the modified EIAG represents more accurate behavior of a program than the EIAG does, test-cases generated by the enhanced method increase the possibility of realizing themselves. The test-cases in the method increase in number. The method, however, is practical in the sense that the number of task-instances generated from a task-type is restricted.