Geometric eccentricity here refers to the radial deviation (radial runout) of pinion or gear geometric center off its rotational center or axis. Such a typical manufacturing or assembly error in gear transmission exhibits inherent effects on the gear dynamic responses. Modeling of eccentricity has rarely been done for high speed right-angle gears such as hypoid or spiral bevel gears. In this paper, two modeling methods are proposed to quantitatively represent the eccentricity in the hypoid/bevel gear dynamic analysis. The first method is based on the loaded tooth contact analysis (LTCA) for a long shaft period. The LTCA results are then used to synthesize the corresponding roll angle dependent varying mesh model parameters. A second simpler method using translational kinematic transmission error (TE) modification is proposed to reduce the computational time. The effects of eccentricity on the gear dynamic responses are then investigated. The eccentricity excited low frequency shaft order dynamics is found to affect not only the overall level of vibration but also the high frequency mesh order responses. The sideband responses are simulated and characterized. This study is expected to improve the right-angle gearing system dynamic analytical capability and assist in guiding the manufacturing or assembly error tolerance specification.