There is a consensus among modern gear researchers that variation in gear mesh stiffness and transmission error are the primary sources of vibratory excitation in most moderately to heavily loaded gear drives. However, several schools of thought exist in the literature on how to incorporate these mesh stiffness and transmission error concepts into a dynamic model. In this paper, a formal expression for an elastic gear mesh force vector is developed and selected gear mesh interface models, which exemplify most of the common modeling approaches in use today, are compared on a common mathematical basis. The various modeling strategies, their inherent philosophies and assumptions are made clear. All of the models examined employ a common spatial domain analysis methodology which pervades the field of modem gear dynamics. The focus of this study is limited to the quasi-steady state, non-resonant dynamic analysis of a single involute gear pair operating below critical shaft speeds such that shaft whirling and gyroscopic effects are negligible, and under loading conditions sufficiently high to prevent loss of tooth contact due to gear backlash phenomenon. The need for extended analytical models, which consider multi-dimensional excitation and better describe force transmissibility via the gear mesh interface, is identified. This forms the basis of an on-going comprehensive investigation which expects to clarify several unresolved issues in gear dynamic modeling; future publications will report such studies.