Hypoid gear whine problems in right-angle driveline components mainly used in rear and all-wheel drive vehicles have frequently posed major concerns in automotive industry. Narrow frequency-band response peaks from the rear axle component at mesh frequency and its harmonics tend to generate high-cost warranty issue and consumer dissatisfaction. In order to develop low noise and vibration geared rotor system, one must have better understanding of the dynamic behavior of these high speed non-parallel precision gears. Hence, it is the objective of this paper to develop a 3-dimensional coupled torsional and translational vibratory model of a generic hypoid gear pair by also taking into account the effect of global driveline system dynamics. In this analytical model, the effective mesh point is assumed to be at the theoretical mean pitch location. Its coordinate and corresponding tooth contact normal vector are determined analytically by applying the theory of hypoid gear kinematics. The resultant formulations for the mesh point and line of action are then incorporated into a dynamic model for a right-angle geared rotor system assuming time-invariant mesh stiffness. The proposed model is used to predict the system modal characteristics and dynamic response due to transmission error excitation for various boundary and operating conditions. A limited set of parametric design studies is also performed to analyze the effects of pinion offset, spiral angle and pinion shaft compliance on torsional and translational vibration response.