This study is focused on a bearing arrangement made of two tapered roller bearings and a shaft, supporting a combination of axial and radial loads. The paper is divided in two parts. This part presents first a numerical procedure to obtain the internal load distribution within tapered roller bearings. The internal load distribution is required to estimate the bearing fatigue life. Afterwards, a numerical method and the related algorithm for a load support system constituted of a shaft and two tapered roller bearings are described. The effect of the initial axial preload (or total axial compression) is taken into account. In consequence the method proposed can be used to select an adequate axial preload in order to increase the system survivability. An example of model implementation, i.e. application to the transfer shaft of an automobile automatic transaxle, is presented in Part 2 of the paper.