The first part of this two-part paper presents an analytical model to predict the performances of double-row tapered roller bearings (DRTRB). The model has been structured in two major parts: (1)- A conventional quasi-static analysis to determine the internal load distribution, the bearing stiffness and the fatigue life and (2)- A quasi-dynamic analysis which integrates the differential equations for each bearing element in order to determine the amount of skidding, the friction forces and moments and consequently the heat dissipation. The proposed model allows one to take into account a general external loading (shaft tilting moments, radial and axial loads), the initial axial compression introduced while mounting, the operating speed and the lubricant properties. Some numerical results are presented in the second part of this two-part paper.