Most tunneling effects are investigate during a one dimensional model, but such an approach fails to explain the phenomena of the propagation of wave in a system with geometric discontinuities. This work studies the tunneling characteristics in a waveguide system that consists of a middle section with a distinct cut or frequency, which is controlled by the cross-sectional geometry. Unlike in the one-dimensional case, in which only the fundamental model is considered, in a virtually three-dimensional system, multiple modes have to be taken into consideration. High-order modes (HOMs) modify the amplitude and the phase of the fundamental mode (TE10), thus subsequently affecting the transmission and group delay of aware. The effect of the high-order evanescent modes is calculated, and the results are compared with the simulated ones using a full-wave solver. Both oversized and undersized waveguides reveal the necessity of considering the HOMs. The underlying physics is manifested during a multiple reflection model. This study indicates that the high-order evanescent modes are essential to the explanation of the phenomena in a tunneling system with geometrical discontinuities.