A numerical model is formulated to analyze the tooth contact dynamic load distribution and dynamic transmission error of a pair of spur gears under the influence of bearing elasticity and gearbox assembly errors. In the proposed model, the deformation of the tooth is computed by applying a combination of finite elements and contact mechanics. The elasticity of the bearings is represented with infinitesimal linear spring elements, while the shafts and gears except the teeth that are in engagement are assumed to be rigid bodies. Applying those assumptions, three sets of highly coupled governing equations representing the meshing teeth flexible behavior, gear-bearing assembly translation dynamics and gear rotation dynamics are derived. The resultant model is then used to predict the dynamical behaviors of the geared rotor system, tooth contact dynamic load, and dynamic transmission error. A set of parametric studies is also performed to analyze the gear dynamic response.