In this paper, inverse problems by the wave equation for a medium with multiple types of cavities with C 2 , θ boundaries is discussed. The previous our result for this problem provides the “shortest lenght”and the “sign of the cavity”for the non-separated case by using the asymptotic solution. However, usual asymptotic solution required the additional regularity assumption for the boundaries of the cavities. Then, a “modified asymptotic solution”is introduced here and the regularity assumption for the boundaries of cavities are relaxed.