Abstract: Hole-coupling technique is a most common design for high power optically-pumped terahertz gas lasers. In this paper, the intra-cavity modes and beam characteristics of the hole-coupling THz resonators have been numerically calculated with a co-called eigenvector method. Several lowest order modes and their diffraction losses of a series of hole-coupling THz resonators with different g parameters are given. The output beam characteristics from the small hole are studied with the diffraction integral associating with the matrix optical method. The far-field distributions and the divergence angles of each mode are computed.